Trắc nghiệm Phương trình lượng giác cơ bản Toán Lớp 11

A. \(x_{0} \in\left(0 ; \frac{\pi}{12}\right)\)

B. \(x_{0} \in\left[\frac{\pi}{12} ; \frac{\pi}{6}\right]\)

C. \(x_{0} \in\left(\frac{\pi}{6} ; \frac{\pi}{3}\right]\)

D. \(x_{0} \in\left(\frac{\pi}{3} ; \frac{\pi}{2}\right]\)

A. \(x_{0} \in\left(-\frac{\pi}{12} ; 0\right)\)

B. \(x_{0} \in\left[-\frac{\pi}{6} ;-\frac{\pi}{12}\right]\)

C. \(x_{0} \in\left[-\frac{\pi}{3} ;-\frac{\pi}{6}\right)\)

D. \(x_{0} \in\left[-\frac{\pi}{2} ;-\frac{\pi}{3}\right)\)

A. \(\left[\begin{array}{l}x=\frac{5 \pi}{6}+k 2 \pi \\ x=\frac{\pi}{18}+k \frac{2 \pi}{3}\end{array}, k \in \mathbb{Z}\right.\)

B. \(\left[\begin{array}{l}x=\frac{7 \pi}{6}+k 2 \pi \\ x=-\frac{\pi}{18}+k \frac{2 \pi}{3}\end{array}, k \in \mathbb{Z}\right.\)

C. \(\left[\begin{array}{l}x=\frac{5 \pi}{6}+k 2 \pi \\ x=\frac{7 \pi}{6}+k 2 \pi\end{array}, k \in \mathbb{Z}\right.\)

D. \(\left[\begin{array}{l}x=\frac{\pi}{18}+k \frac{2 \pi}{3} \\ x=-\frac{\pi}{18}+k \frac{2 \pi}{3}\end{array}, k \in \mathbb{Z}\right.\)

A. 1

B. 2

C. 3

D. 4

A. \(x_{0}=\frac{\pi}{2}\)

B. \(x_{0}=\frac{\pi}{18}\)

C. \(x_{0}=\frac{\pi}{24}\)

D. \(x_{0}=\frac{\pi}{54}\)

A. \(T=\frac{7 \pi}{8}\)

B. \(T=\frac{21 \pi}{8}\)

C. \(T=\frac{11 \pi}{4}\)

D. \(T=\frac{3 \pi}{4}\)

A. \(\frac{5 \pi}{6}\)

B. \(\frac{\pi}{2}\)

C. \(\frac{7 \pi}{6}\)

D. \(\frac{\pi}{6}\)

A. \(\frac{\pi}{9}\)

B. \(-\frac{\pi}{6}\)

C. \(\frac{\pi}{6}\)

D. \(-\frac{\pi}{9}\)

A. 4034.

B. 4035.

C. 641.  

D. 642.

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE % cacaGGOaGaamiEaiaacMcacqGH9aqpdaGabaabaeqabaGaamiEamaa % CaaaleqabaGaaGOmaaaakiGacohacaGGPbGaaiOBamaalaaabaGaaG % ymaaqaaiaadIhaaaGaeyOeI0IaamiEaiGacogacaGGVbGaai4Camaa % laaabaGaaGymaaqaaiaadIhaaaGaaeiiaiaabccacaqGGaGaae4Aai % aabIgacaqGPbGaaeiiaiaadIhacqGHGjsUcaaIWaaabaGaaeimaiaa % bccacaqGGaGaaeiiaiaabccacaqGGaGaae4AaiaabIgacaqGPbGaae % iiaiaabccacaqGGaGaamiEaiabg2da9iaaicdaaaGaay5Eaaaaaa!5D38! f'(x) = \left\{ \begin{array}{l} {x^2}\sin \frac{1}{x} - x\cos \frac{1}{x}{\rm{ khi }}x \ne 0\\ {\rm{0 khi }}x = 0 \end{array} \right.\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE % cacaGGOaGaamiEaiaacMcacqGH9aqpdaGabaabaeqabaGaaG4maiaa % dIhadaahaaWcbeqaaiaaikdaaaGcciGGZbGaaiyAaiaac6gadaWcaa % qaaiaaigdaaeaacaWG4baaaiabgkHiTiaadIhaciGGJbGaai4Baiaa % cohadaWcaaqaaiaaigdaaeaacaWG4baaaiaabccacaqGGaGaaeiiai % aabUgacaqGObGaaeyAaiaabccacaWG4bGaeyiyIKRaaGimaaqaaiaa % icdacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabUgacaqGObGaae % yAaiaabccacaqGGaGaaeiiaiaadIhacqGH9aqpcaaIWaaaaiaawUha % aaaa!5DFC! f'(x) = \left\{ \begin{array}{l} 3{x^2}\sin \frac{1}{x} - x\cos \frac{1}{x}{\rm{ khi }}x \ne 0\\ 0{\rm{ khi }}x = 0 \end{array} \right.\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE % cacaGGOaGaamiEaiaacMcacqGH9aqpdaGabaabaeqabaGaaG4maiaa % dIhadaahaaWcbeqaaiaaikdaaaGcciGGZbGaaiyAaiaac6gadaWcaa % qaaiaaigdaaeaacaWG4baaaiabgUcaRiaadIhaciGGJbGaai4Baiaa % cohadaWcaaqaaiaaigdaaeaacaWG4baaaiaabccacaqGGaGaaeiiai % aabUgacaqGObGaaeyAaiaabccacaWG4bGaeyiyIKRaaGimaaqaaiaa % icdacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabUgacaqGObGaae % yAaiaabccacaqGGaGaaeiiaiaadIhacqGH9aqpcaaIWaaaaiaawUha % aaaa!5DF1! f'(x) = \left\{ \begin{array}{l} 3{x^2}\sin \frac{1}{x} + x\cos \frac{1}{x}{\rm{ khi }}x \ne 0\\ 0{\rm{ khi }}x = 0 \end{array} \right.\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE % cacaGGOaGaamiEaiaacMcacqGH9aqpdaGabaabaeqabaGaaG4maiaa % dIhadaahaaWcbeqaaiaaikdaaaGcciGGZbGaaiyAaiaac6gadaWcaa % qaaiaaigdaaeaacaWG4baaaiabgkHiTiGacogacaGGVbGaai4Camaa % laaabaGaaGymaaqaaiaadIhaaaGaaeiiaiaabccacaqGGaGaae4Aai % aabIgacaqGPbGaaeiiaiaadIhacqGHGjsUcaaIWaaabaGaaGimaiaa % bccacaqGGaGaaeiiaiaabccacaqGGaGaae4AaiaabIgacaqGPbGaae % iiaiaabccacaqGGaGaamiEaiabg2da9iaaicdaaaGaay5Eaaaaaa!5CFF! f'(x) = \left\{ \begin{array}{l} 3{x^2}\sin \frac{1}{x} - \cos \frac{1}{x}{\rm{ khi }}x \ne 0\\ 0{\rm{ khi }}x = 0 \end{array} \right.\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaGkadaWcaa % qaaiGacohacaGGPbGaaiOBaiaaikdacaWG4baabaGaci4yaiaac+ga % caGGZbWaaWbaaSqabeaacaaIYaaaaOGaaGOmaiaadIhaaaGaaiOlaa % aa!4171! \frac{{\sin 2x}}{{{{\cos }^2}2x}}.\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci % GGZbGaaiyAaiaac6gacaWG4baabaGaci4yaiaac+gacaGGZbWaaWba % aSqabeaacaaIYaaaaOGaaGOmaiaadIhaaaGaaiOlaaaa!400A! \frac{{\sin x}}{{{{\cos }^2}2x}}.\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIYaGaci4yaiaac+gacaGGZbGaaGOmaiaadIhaaeaaciGGZbGaaiyA % aiaac6gadaahaaWcbeqaaiaaikdaaaGccaaIYaGaamiEaaaacaGGUa % aaaa!4181! \frac{{2\cos 2x}}{{{{\sin }^2}2x}}.\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIYaGaci4CaiaacMgacaGGUbGaaGOmaiaadIhaaeaaciGGJbGaai4B % aiaacohadaahaaWcbeqaaiaaikdaaaGccaaIYaGaamiEaaaacaGGUa % aaaa!4182! \frac{{2\sin 2x}}{{{{\cos }^2}2x}}.\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aI2aaabaWaaeWaaeaacaaIYaGaci4CaiaacMgacaGGUbGaaGOmaiaa % dIhacqGHsislciGGJbGaai4BaiaacohacaaIYaGaamiEaaGaayjkai % aawMcaamaaCaaaleqabaGaaGOmaaaaaaaaaa!43FC! \frac{6}{{{{\left( {2\sin 2x - \cos 2x} \right)}^2}}}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaaI2aaabaWaaeWaaeaaciGGZbGaaiyAaiaac6gacaaIYaGa % amiEaiabgkHiTiGacogacaGGVbGaai4CaiaaikdacaWG4baacaGLOa % GaayzkaaWaaWbaaSqabeaacaaIYaaaaaaaaaa!442D! \frac{{ - 6}}{{{{\left( {\sin 2x - \cos 2x} \right)}^2}}}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aI2aaabaWaaeWaaeaacaaIYaGaci4CaiaacMgacaGGUbGaaGOmaiaa % dIhacqGHsislciGGJbGaai4BaiaacohacaWG4baacaGLOaGaayzkaa % WaaWbaaSqabeaacaaIYaaaaaaaaaa!4340! \frac{6}{{{{\left( {2\sin 2x - \cos x} \right)}^2}}}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaaI2aaabaWaaeWaaeaacaaIYaGaci4CaiaacMgacaGGUbGa % aGOmaiaadIhacqGHsislciGGJbGaai4BaiaacohacaaIYaGaamiEaa % GaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaaaaaa!44E9! \frac{{ - 6}}{{{{\left( {2\sin 2x - \cos 2x} \right)}^2}}}\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaigdaaeaadaGcaaqaaiaadIhaaSqabaGc % daqadaqaamaakaaabaGaamiEaaWcbeaakiabgkHiTiaaigdaaiaawI % cacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaOGaaiOlaiGacohacaGG % PbGaaiOBamaabmaabaWaaSaaaeaadaGcaaqaaiaadIhaaSqabaGccq % GHRaWkcaaIXaaabaWaaOaaaeaacaWG4baaleqaaOGaeyOeI0IaaGym % aaaaaiaawIcacaGLPaaacaGGUaaaaa!4B34! y' = \frac{1}{{\sqrt x {{\left( {\sqrt x - 1} \right)}^2}}}.\sin \left( {\frac{{\sqrt x + 1}}{{\sqrt x - 1}}} \right).\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaigdaaeaadaGcaaqaaiaadIhaaSqabaGc % daqadaqaamaakaaabaGaamiEaaWcbeaakiabgkHiTiaaigdaaiaawI % cacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaOGaaiOlaiGacogacaGG % VbGaai4CamaabmaabaGaaGOmaiaac6cadaWcaaqaamaakaaabaGaam % iEaaWcbeaakiabgUcaRiaaigdaaeaadaGcaaqaaiaadIhaaSqabaGc % cqGHsislcaaIXaaaaaGaayjkaiaawMcaaiaac6caaaa!4C9C! y' = \frac{1}{{\sqrt x {{\left( {\sqrt x - 1} \right)}^2}}}.\cos \left( {2.\frac{{\sqrt x + 1}}{{\sqrt x - 1}}} \right).\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaigdaaeaadaGcaaqaaiaadIhaaSqabaGc % daqadaqaamaakaaabaGaamiEaaWcbeaakiabgkHiTiaaigdaaiaawI % cacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaOGaaiOlaiGacohacaGG % PbGaaiOBamaabmaabaGaaGOmaiaac6cadaWcaaqaamaakaaabaGaam % iEaaWcbeaakiabgkHiTiaaigdaaeaadaGcaaqaaiaadIhaaSqabaGc % cqGHRaWkcaaIXaaaaaGaayjkaiaawMcaaiaac6caaaa!4CA2! y' = \frac{1}{{\sqrt x {{\left( {\sqrt x - 1} \right)}^2}}}.\sin \left( {2.\frac{{\sqrt x - 1}}{{\sqrt x + 1}}} \right).\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaigdaaeaadaGcaaqaaiaadIhaaSqabaGc % daqadaqaamaakaaabaGaamiEaaWcbeaakiabgkHiTiaaigdaaiaawI % cacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaOGaaiOlaiGacohacaGG % PbGaaiOBamaabmaabaGaaGOmaiaac6cadaWcaaqaamaakaaabaGaam % iEaaWcbeaakiabgUcaRiaaigdaaeaadaGcaaqaaiaadIhaaSqabaGc % cqGHsislcaaIXaaaaaGaayjkaiaawMcaaiaac6caaaa!4CA2! y' = \frac{1}{{\sqrt x {{\left( {\sqrt x - 1} \right)}^2}}}.\sin \left( {2.\frac{{\sqrt x + 1}}{{\sqrt x - 1}}} \right).\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci % GGZbGaaiyAaiaac6gadaahaaWcbeqaaiaaikdaaaGccaWG4baabaWa % aeWaaeaacaaIXaGaey4kaSIaci4yaiaac+gacaGGZbGaamiEaaGaay % jkaiaawMcaamaaCaaaleqabaGaaG4maaaaaaaaaa!42AC! \frac{{{{\sin }^2}x}}{{{{\left( {1 + \cos x} \right)}^3}}}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIZaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaamiE % aaqaamaabmaabaGaaGymaiabgUcaRiGacogacaGGVbGaai4CaiaadI % haaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaaaa!4368! \frac{{3{{\sin }^2}x}}{{{{\left( {1 + \cos x} \right)}^2}}}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIYaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaamiE % aaqaamaabmaabaGaaGymaiabgUcaRiGacogacaGGVbGaai4CaiaadI % haaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaaaa!4367! \frac{{2{{\sin }^2}x}}{{{{\left( {1 + \cos x} \right)}^2}}}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIZaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaamiE % aaqaamaabmaabaGaaGymaiabgUcaRiGacogacaGGVbGaai4CaiaadI % haaiaawIcacaGLPaaadaahaaWcbeqaaiaaiodaaaaaaaaa!4369! \frac{{3{{\sin }^2}x}}{{{{\left( {1 + \cos x} \right)}^3}}}\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaiodacaWG4bWaaWbaaSqabeaacaaIYaaa % aOGaey4kaSIaaGioaiGacogacaGGVbGaai4CamaaCaaaleqabaGaaG % 4maaaakiaacIcacaaIYaGaamiEaiabgkHiTmaalaaabaGaeqiWdaha % baGaaGinaaaacaGGPaGaci4CaiaacMgacaGGUbGaaiikaiaaikdaca % WG4bGaeyOeI0YaaSaaaeaacqaHapaCaeaacaaI0aaaaiaacMcaaeaa % caaIZaWaaOqaaeaadaqadaqaaiaadIhadaahaaWcbeqaaiaaiodaaa % GccqGHRaWkciGGJbGaai4BaiaacohadaahaaWcbeqaaiaaisdaaaGc % caGGOaGaaGOmaiaadIhacqGHsisldaWcaaqaaiabec8aWbqaaiaaio % daaaGaaiykaaGaayjkaiaawMcaamaaCaaaleqabaGaaG4maaaaaeaa % caaIZaaaaaaaaaa!61D8! y' = \frac{{3{x^2} + 8{{\cos }^3}(2x - \frac{\pi }{4})\sin (2x - \frac{\pi }{4})}}{{3\sqrt[3]{{{{\left( {{x^3} + {{\cos }^4}(2x - \frac{\pi }{3})} \right)}^3}}}}}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaiodacaWG4bWaaWbaaSqabeaacaaIYaaa % aOGaeyOeI0IaaGioaiGacogacaGGVbGaai4CamaaCaaaleqabaGaaG % 4maaaakiaacIcacaaIYaGaamiEaiabgkHiTmaalaaabaGaeqiWdaha % baGaaGinaaaacaGGPaGaci4CaiaacMgacaGGUbGaaiikaiaaikdaca % WG4bGaeyOeI0YaaSaaaeaacqaHapaCaeaacaaI0aaaaiaacMcaaeaa % caaI0aWaaOqaaeaadaqadaqaaiaadIhadaahaaWcbeqaaiaaiodaaa % GccqGHRaWkciGGJbGaai4BaiaacohadaahaaWcbeqaaiaaisdaaaGc % caGGOaGaaGOmaiaadIhacqGHsisldaWcaaqaaiabec8aWbqaaiaaio % daaaGaaiykaaGaayjkaiaawMcaamaaCaaaleqabaGaaG4maaaaaeaa % caaIZaaaaaaaaaa!61E4! y' = \frac{{3{x^2} - 8{{\cos }^3}(2x - \frac{\pi }{4})\sin (2x - \frac{\pi }{4})}}{{4\sqrt[3]{{{{\left( {{x^3} + {{\cos }^4}(2x - \frac{\pi }{3})} \right)}^3}}}}}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaiAdacaWG4bWaaWbaaSqabeaacaaIYaaa % aOGaeyOeI0IaaGioaiGacogacaGGVbGaai4CamaaCaaaleqabaGaaG % 4maaaakiaacIcacaaIYaGaamiEaiabgkHiTmaalaaabaGaeqiWdaha % baGaaGinaaaacaGGPaGaci4CaiaacMgacaGGUbGaaiikaiaaikdaca % WG4bGaeyOeI0YaaSaaaeaacqaHapaCaeaacaaI0aaaaiaacMcaaeaa % caaIZaWaaOqaaeaadaqadaqaaiaadIhadaahaaWcbeqaaiaaiodaaa % GccqGHRaWkciGGJbGaai4BaiaacohadaahaaWcbeqaaiaaisdaaaGc % caGGOaGaaGOmaiaadIhacqGHsisldaWcaaqaaiabec8aWbqaaiaaio % daaaGaaiykaaGaayjkaiaawMcaamaaCaaaleqabaGaaG4maaaaaeaa % caaIZaaaaaaaaaa!61E6! y' = \frac{{6{x^2} - 8{{\cos }^3}(2x - \frac{\pi }{4})\sin (2x - \frac{\pi }{4})}}{{3\sqrt[3]{{{{\left( {{x^3} + {{\cos }^4}(2x - \frac{\pi }{3})} \right)}^3}}}}}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaiodacaWG4bWaaWbaaSqabeaacaaIYaaa % aOGaeyOeI0IaaGioaiGacogacaGGVbGaai4CamaaCaaaleqabaGaaG % 4maaaakiaacIcacaaIYaGaamiEaiabgkHiTmaalaaabaGaeqiWdaha % baGaaGinaaaacaGGPaGaci4CaiaacMgacaGGUbGaaiikaiaaikdaca % WG4bGaeyOeI0YaaSaaaeaacqaHapaCaeaacaaI0aaaaiaacMcaaeaa % caaIZaWaaOqaaeaadaqadaqaaiaadIhadaahaaWcbeqaaiaaiodaaa % GccqGHRaWkciGGJbGaai4BaiaacohadaahaaWcbeqaaiaaisdaaaGc % caGGOaGaaGOmaiaadIhacqGHsisldaWcaaqaaiabec8aWbqaaiaaio % daaaGaaiykaaGaayjkaiaawMcaamaaCaaaleqabaGaaG4maaaaaeaa % caaIZaaaaaaaaaa!61E3! y' = \frac{{3{x^2} - 8{{\cos }^3}(2x - \frac{\pi }{4})\sin (2x - \frac{\pi }{4})}}{{3\sqrt[3]{{{{\left( {{x^3} + {{\cos }^4}(2x - \frac{\pi }{3})} \right)}^3}}}}}\)

A. 3sin(6x + 2)

B. sin(6x+2)

C. -3sin(6x + 2)

D. 3cos(6x+2)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aI1aGaey4kaSIaaGOmaiGacshacaGGHbGaaiOBamaaCaaaleqabaGa % aGOmaaaakiaadIhaaeaacaaIYaWaaOaaaeaacaaIZaGaamiEaiabgU % caRiaaikdaciGG0bGaaiyyaiaac6gacaWG4baaleqaaaaaaaa!451F! \frac{{5 + 2{{\tan }^2}x}}{{2\sqrt {3x + 2\tan x} }}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aI1aGaeyOeI0IaaGOmaiGacshacaGGHbGaaiOBamaaCaaaleqabaGa % aGOmaaaakiaadIhaaeaacaaIYaWaaOaaaeaacaaIZaGaamiEaiabgU % caRiaaikdaciGG0bGaaiyyaiaac6gacaWG4baaleqaaaaaaaa!452A! \frac{{5 - 2{{\tan }^2}x}}{{2\sqrt {3x + 2\tan x} }}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaaI1aGaey4kaSIaaGOmaiGacshacaGGHbGaaiOBamaaCaaa % leqabaGaaGOmaaaakiaadIhaaeaacaaIYaWaaOaaaeaacaaIZaGaam % iEaiabgUcaRiaaikdaciGG0bGaaiyyaiaac6gacaWG4baaleqaaaaa % aaa!460C! \frac{{ - 5 + 2{{\tan }^2}x}}{{2\sqrt {3x + 2\tan x} }}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaaI1aGaeyOeI0IaaGOmaiGacshacaGGHbGaaiOBamaaCaaa % leqabaGaaGOmaaaakiaadIhaaeaacaaIYaWaaOaaaeaacaaIZaGaam % iEaiabgUcaRiaaikdaciGG0bGaaiyyaiaac6gacaWG4baaleqaaaaa % aaa!4617! \frac{{ - 5 - 2{{\tan }^2}x}}{{2\sqrt {3x + 2\tan x} }}\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS % aaaeaacaaIXaGaey4kaSIaci4CaiaacMgacaGGUbWaaWbaaSqabeaa % caaIYaaaaOGaamiEaaqaaiaaikdaciGGZbGaaiyAaiaac6gadaahaa % WcbeqaaiaaiodaaaGccaWG4baaaaaa!42DB! - \frac{{1 + {{\sin }^2}x}}{{2{{\sin }^3}x}}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS % aaaeaacaaIXaGaey4kaSIaci4yaiaac+gacaGGZbWaaWbaaSqabeaa % caaIYaaaaOGaamiEaaqaaiaaikdaciGGZbGaaiyAaiaac6gadaahaa % WcbeqaaiaaiodaaaGccaWG4baaaaaa!42D6! - \frac{{1 + {{\cos }^2}x}}{{2{{\sin }^3}x}}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaGaey4kaSIaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaa % aOGaamiEaaqaaiaaikdaciGGZbGaaiyAaiaac6gadaahaaWcbeqaai % aaiodaaaGccaWG4baaaaaa!41EE! \frac{{1 + {{\sin }^2}x}}{{2{{\sin }^3}x}}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaGaey4kaSIaci4yaiaac+gacaGGZbWaaWbaaSqabeaacaaIYaaa % aOGaamiEaaqaaiaaikdaciGGZbGaaiyAaiaac6gadaahaaWcbeqaai % aaiodaaaGccaWG4baaaaaa!41E9! \frac{{1 + {{\cos }^2}x}}{{2{{\sin }^3}x}}\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaGaamiEaiGacshacaGGHbGaaiOBaiaadIhacqGH % RaWkdaWcaaqaaiaaigdaaeaacaaIYaWaaOaaaeaacaWG4baaleqaaa % aakiaac6caaaa!4266! y' = 2x\tan x + \frac{1}{{2\sqrt x }}.\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIYaaabaGaaG4maaaaaaa!377C! \frac{2}{3}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaGaamiEaiGacshacaGGHbGaaiOBaiaadIhacqGH % RaWkdaWcaaqaaiaadIhadaahaaWcbeqaaiaaikdaaaaakeaaciGGJb % Gaai4BaiaacohadaahaaWcbeqaaiaaikdaaaGccaWG4baaaiabgUca % RmaalaaabaGaaGymaaqaaiaaikdadaGcaaqaaiaadIhaaSqabaaaaO % GaaiOlaaaa!4A0B! y' = 2x\tan x + \frac{{{x^2}}}{{{{\cos }^2}x}} + \frac{1}{{2\sqrt x }}.\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaGaamiEaiGacshacaGGHbGaaiOBaiaadIhacqGH % RaWkdaWcaaqaaiaadIhadaahaaWcbeqaaiaaikdaaaaakeaaciGGJb % Gaai4BaiaacohadaahaaWcbeqaaiaaikdaaaGccaWG4baaaiabgUca % RmaalaaabaGaaGymaaqaamaakaaabaGaamiEaaWcbeaaaaGccaGGUa % aaaa!494F! y' = 2x\tan x + \frac{{{x^2}}}{{{{\cos }^2}x}} + \frac{1}{{\sqrt x }}.\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcqGHsislcaaIYaGaci4yaiaac+gacaGG0bWaaeWaaeaa % ciGGJbGaai4BaiaacohacaWG4baacaGLOaGaayzkaaWaaSaaaeaaca % aIXaaabaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOWa % aeWaaeaaciGGJbGaai4BaiaacohacaWG4baacaGLOaGaayzkaaaaai % abgUcaRmaalaaabaGaci4yaiaac+gacaGGZbGaamiEaaqaaiaaikda % daGcaaqaaiGacohacaGGPbGaaiOBaiaadIhacqGHsisldaWcaaqaai % abec8aWbqaaiaaikdaaaaaleqaaaaakiaac6caaaa!5A07! y' = - 2\cot \left( {\cos x} \right)\frac{1}{{{{\sin }^2}\left( {\cos x} \right)}} + \frac{{\cos x}}{{2\sqrt {\sin x - \frac{\pi }{2}} }}.\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaGaci4yaiaac+gacaGG0bWaaeWaaeaaciGGJbGa % ai4BaiaacohacaWG4baacaGLOaGaayzkaaWaaSaaaeaacaaIXaaaba % Gaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOWaaeWaaeaa % ciGGJbGaai4BaiaacohacaWG4baacaGLOaGaayzkaaaaaiaac6caci % GGZbGaaiyAaiaac6gacaWG4bGaey4kaSYaaSaaaeaaciGGJbGaai4B % aiaacohacaWG4baabaGaaGOmamaakaaabaGaci4CaiaacMgacaGGUb % GaamiEaiabgkHiTmaalaaabaGaeqiWdahabaGaaGOmaaaaaSqabaaa % aOGaaiOlaaaa!5DA1! y' = 2\cot \left( {\cos x} \right)\frac{1}{{{{\sin }^2}\left( {\cos x} \right)}}.\sin x + \frac{{\cos x}}{{2\sqrt {\sin x - \frac{\pi }{2}} }}.\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcqGHsislcaaIYaGaci4yaiaac+gacaGG0bWaaeWaaeaa % ciGGJbGaai4BaiaacohacaWG4baacaGLOaGaayzkaaWaaSaaaeaaca % aIXaaabaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOWa % aeWaaeaaciGGJbGaai4BaiaacohacaWG4baacaGLOaGaayzkaaaaai % abgUcaRmaalaaabaGaci4yaiaac+gacaGGZbGaamiEaaqaamaakaaa % baGaci4CaiaacMgacaGGUbGaamiEaiabgkHiTmaalaaabaGaeqiWda % habaGaaGOmaaaaaSqabaaaaOGaaiOlaaaa!594B! y' = - 2\cot \left( {\cos x} \right)\frac{1}{{{{\sin }^2}\left( {\cos x} \right)}} + \frac{{\cos x}}{{\sqrt {\sin x - \frac{\pi }{2}} }}.\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaGaci4yaiaac+gacaGG0bWaaeWaaeaaciGGJbGa % ai4BaiaacohacaWG4baacaGLOaGaayzkaaWaaSaaaeaacaaIXaaaba % Gaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOWaaeWaaeaa % ciGGJbGaai4BaiaacohacaWG4baacaGLOaGaayzkaaaaaiaac6caci % GGZbGaaiyAaiaac6gacaWG4bGaey4kaSYaaSaaaeaaciGGJbGaai4B % aiaacohacaWG4baabaWaaOaaaeaaciGGZbGaaiyAaiaac6gacaWG4b % GaeyOeI0YaaSaaaeaacqaHapaCaeaacaaIYaaaaaWcbeaaaaGccaGG % Uaaaaa!5CE5! y' = 2\cot \left( {\cos x} \right)\frac{1}{{{{\sin }^2}\left( {\cos x} \right)}}.\sin x + \frac{{\cos x}}{{\sqrt {\sin x - \frac{\pi }{2}} }}.\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0ZaaSaaaeaacaaIXaaabaGaaGOmamaakaaabaGaaGOmaiab % gUcaRiGacshacaGGHbGaaiOBamaabmaabaGaamiEaiabgUcaRmaala % aabaGaaGymaaqaaiaadIhaaaaacaGLOaGaayzkaaaaleqaaaaakiab % gwSixdaa!4598! y' = \frac{1}{{2\sqrt {2 + \tan \left( {x + \frac{1}{x}} \right)} }} \cdot \)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0ZaaSaaaeaacaaIXaGaey4kaSIaciiDaiaacggacaGGUbWa % aWbaaSqabeaacaaIYaaaaOWaaeWaaeaacaWG4bGaey4kaSYaaSaaae % aacaaIXaaabaGaamiEaaaaaiaawIcacaGLPaaaaeaacaaIYaWaaOaa % aeaacaaIYaGaey4kaSIaciiDaiaacggacaGGUbWaaeWaaeaacaWG4b % Gaey4kaSYaaSaaaeaacaaIXaaabaGaamiEaaaaaiaawIcacaGLPaaa % aSqabaaaaOGaeyyXICnaaa!4F6E! y' = \frac{{1 + {{\tan }^2}\left( {x + \frac{1}{x}} \right)}}{{2\sqrt {2 + \tan \left( {x + \frac{1}{x}} \right)} }} \cdot \)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0ZaaSaaaeaacaaIXaGaey4kaSIaciiDaiaacggacaGGUbWa % aWbaaSqabeaacaaIYaaaaOWaaeWaaeaacaWG4bGaey4kaSYaaSaaae % aacaaIXaaabaGaamiEaaaaaiaawIcacaGLPaaaaeaacaaIYaWaaOaa % aeaacaaIYaGaey4kaSIaciiDaiaacggacaGGUbWaaeWaaeaacaWG4b % Gaey4kaSYaaSaaaeaacaaIXaaabaGaamiEaaaaaiaawIcacaGLPaaa % aSqabaaaaOGaaiOlamaabmaabaGaaGymaiabgkHiTmaalaaabaGaaG % ymaaqaaiaadIhadaahaaWcbeqaaiaaikdaaaaaaaGccaGLOaGaayzk % aaGaaiOlaaaa!5474! y' = \frac{{1 + {{\tan }^2}\left( {x + \frac{1}{x}} \right)}}{{2\sqrt {2 + \tan \left( {x + \frac{1}{x}} \right)} }}.\left( {1 - \frac{1}{{{x^2}}}} \right).\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0ZaaSaaaeaacaaIXaGaey4kaSIaciiDaiaacggacaGGUbWa % aWbaaSqabeaacaaIYaaaaOWaaeWaaeaacaWG4bGaey4kaSYaaSaaae % aacaaIXaaabaGaamiEaaaaaiaawIcacaGLPaaaaeaacaaIYaWaaOaa % aeaacaaIYaGaey4kaSIaciiDaiaacggacaGGUbWaaeWaaeaacaWG4b % Gaey4kaSYaaSaaaeaacaaIXaaabaGaamiEaaaaaiaawIcacaGLPaaa % aSqabaaaaOGaaiOlamaabmaabaGaaGymaiabgUcaRmaalaaabaGaaG % ymaaqaaiaadIhadaahaaWcbeqaaiaaikdaaaaaaaGccaGLOaGaayzk % aaGaaiOlaaaa!5469! y' = \frac{{1 + {{\tan }^2}\left( {x + \frac{1}{x}} \right)}}{{2\sqrt {2 + \tan \left( {x + \frac{1}{x}} \right)} }}.\left( {1 + \frac{1}{{{x^2}}}} \right).\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaeyOeI0IaaGOmaiGacohacaGGPbGaaiOBamaabmaabaGa % eqiWdaNaeyOeI0IaaGinaiaadIhaaiaawIcacaGLPaaacqGHRaWkda % Wcaaqaaiabec8aWbqaaiaaikdaaaGaeyyXICnaaa!4827! y' = - 2\sin \left( {\pi - 4x} \right) + \frac{\pi }{2} \cdot \)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaaGOmaiGacohacaGGPbGaaiOBamaabmaabaWaaSaaaeaa % cqaHapaCaeaacaaIYaaaaiabgkHiTiaadIhaaiaawIcacaGLPaaaci % GGJbGaai4BaiaacohadaqadaqaamaalaaabaGaeqiWdahabaGaaGOm % aaaacqGHsislcaWG4baacaGLOaGaayzkaaGaey4kaSYaaSaaaeaacq % aHapaCaeaacaaIYaaaaiaac6caaaa!4E7F! y' = 2\sin \left( {\frac{\pi }{2} - x} \right)\cos \left( {\frac{\pi }{2} - x} \right) + \frac{\pi }{2}.\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaaGOmaiGacohacaGGPbGaaiOBamaabmaabaWaaSaaaeaa % cqaHapaCaeaacaaIYaaaaiabgkHiTiaadIhaaiaawIcacaGLPaaaci % GGJbGaai4BaiaacohadaqadaqaamaalaaabaGaeqiWdahabaGaaGOm % aaaacqGHsislcaWG4baacaGLOaGaayzkaaGaey4kaSYaaSaaaeaacq % aHapaCaeaacaaIYaaaaiaadIhacaGGUaaaaa!4F7C! y' = 2\sin \left( {\frac{\pi }{2} - x} \right)\cos \left( {\frac{\pi }{2} - x} \right) + \frac{\pi }{2}x.\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaeyOeI0IaaGOmaiGacohacaGGPbGaaiOBamaabmaabaGa % eqiWdaNaeyOeI0IaaGinaiaadIhaaiaawIcacaGLPaaacaGGUaaaaa!4324! y' = - 2\sin \left( {\pi - 4x} \right).\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aI0aGaamiEaaqaaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOm % aaaakmaabmaabaGaaGymaiabgkHiTiaaikdacaWG4baacaGLOaGaay % zkaaaaaaaa!4074! \frac{{4x}}{{{{\sin }^2}\left( {1 - 2x} \right)}}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaaI0aaabaGaci4CaiaacMgacaGGUbWaaeWaaeaacaaIXaGa % eyOeI0IaaGOmaiaadIhaaiaawIcacaGLPaaaaaaaaa!3F71! \frac{{ - 4}}{{\sin \left( {1 - 2x} \right)}}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaaI0aGaamiEaaqaaiGacohacaGGPbGaaiOBamaaCaaaleqa % baGaaGOmaaaakmaabmaabaGaaGymaiabgkHiTiaaikdacaWG4baaca % GLOaGaayzkaaaaaaaa!4161! \frac{{ - 4x}}{{{{\sin }^2}\left( {1 - 2x} \right)}}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaaI0aaabaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaI % YaaaaOWaaeWaaeaacaaIXaGaeyOeI0IaaGOmaiaadIhaaiaawIcaca % GLPaaaaaaaaa!4064! \frac{{ - 4}}{{{{\sin }^2}\left( {1 - 2x} \right)}}\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaWG4bGaey4kaSYaaSaaaeaacaaIXaaabaGaaGOmaaaaciGGJbGa % ai4BaiaacohacaaIYaGaamiEaaaa!3E05! x + \frac{1}{2}\cos 2x\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabgk % HiTmaalaaabaGaaGymaaqaaiaaikdaaaGaci4yaiaac+gacaGGZbGa % aGOmaiaadIhaaaa!3DF1! x - \frac{1}{2}\cos 2x\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaWG4bGaeyOeI0Iaci4CaiaacMgacaGGUbGaaGOmaiaadIhaaaa!3C8E! x - \sin 2x\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaWG4bGaeyOeI0Iaci4CaiaacMgacaGGUbGaaGOmaiaadIhaaaa!3C8E! x + \sin 2x\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaaGOmamaalaaabaGaciiDaiaacggacaGGUbGaamiEaaqa % aiGacogacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakiaadIhaaa % Gaey4kaSIaaGOmamaalaaabaGaci4yaiaac+gacaGG0bGaamiEaaqa % aiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaadIhaaa % GaeyyXICnaaa!4DF1! y' = 2\frac{{\tan x}}{{{{\cos }^2}x}} + 2\frac{{\cot x}}{{{{\sin }^2}x}} \cdot \)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaaGOmamaalaaabaGaciiDaiaacggacaGGUbGaamiEaaqa % aiGacogacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakiaadIhaaa % GaeyOeI0IaaGOmamaalaaabaGaci4yaiaac+gacaGG0bGaamiEaaqa % aiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaadIhaaa % GaeyyXICnaaa!4DFC! y' = 2\frac{{\tan x}}{{{{\cos }^2}x}} - 2\frac{{\cot x}}{{{{\sin }^2}x}} \cdot \)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaaGOmamaalaaabaGaciiDaiaacggacaGGUbGaamiEaaqa % aiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaadIhaaa % Gaey4kaSIaaGOmamaalaaabaGaci4yaiaac+gacaGG0bGaamiEaaqa % aiGacogacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakiaadIhaaa % GaeyyXICnaaa!4DF1! y' = 2\frac{{\tan x}}{{{{\sin }^2}x}} + 2\frac{{\cot x}}{{{{\cos }^2}x}} \cdot \)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaaGOmaiGacshacaGGHbGaaiOBaiaadIhacqGHsislcaaI % YaGaci4yaiaac+gacaGG0bGaamiEaiaac6caaaa!42B9! y' = 2\tan x - 2\cot x.\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaaGOmaiGacohacaGGPbGaaiOBaiaaikdacaWG4bGaaiOl % aiGacogacaGGVbGaai4CaiaadIhacqGHsislciGGZbGaaiyAaiaac6 % gacaWG4bGaaiOlaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOm % aaaakiaaikdacaWG4bGaeyOeI0IaaGOmamaakaaabaGaamiEaaWcbe % aakiaac6caaaa!5047! y' = 2\sin 2x.\cos x - \sin x.{\sin ^2}2x - 2\sqrt x .\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaaGOmaiGacohacaGGPbGaaiOBaiaaikdacaWG4bGaaiOl % aiGacogacaGGVbGaai4CaiaadIhacqGHsislciGGZbGaaiyAaiaac6 % gacaWG4bGaaiOlaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOm % aaaakiaaikdacaWG4bGaeyOeI0IaaGOmamaakaaabaGaamiEaaWcbe % aakiaac6caaaa!5047! y' = 2\sin 2x.\cos x - \sin x.{\sin ^2}2x - 2\sqrt x .\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaaGOmaiGacohacaGGPbGaaiOBaiaaisdacaWG4bGaaiOl % aiGacogacaGGVbGaai4CaiaadIhacqGHRaWkciGGZbGaaiyAaiaac6 % gacaWG4bGaaiOlaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOm % aaaakiaaikdacaWG4bGaeyOeI0YaaSaaaeaacaaIXaaabaGaamiEam % aakaaabaGaamiEaaWcbeaaaaGccqGHflY1aaa!52E2! y' = 2\sin 4x.\cos x + \sin x.{\sin ^2}2x - \frac{1}{{x\sqrt x }} \cdot \)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JaaGOmaiGacohacaGGPbGaaiOBaiaaisdacaWG4bGaaiOl % aiGacogacaGGVbGaai4CaiaadIhacqGHsislciGGZbGaaiyAaiaac6 % gacaWG4bGaaiOlaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOm % aaaakiaaikdacaWG4bGaeyOeI0YaaSaaaeaacaaIXaaabaGaamiEam % aakaaabaGaamiEaaWcbeaaaaGccqGHflY1aaa!52ED! y' = \sin 4x.\cos x - \sin x.{\sin ^2}2x - \frac{1}{{x\sqrt x }} \cdot \)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaigdacqGHRaWkciGGJbGaai4Baiaacsha % daahaaWcbeqaaiaaikdaaaGccaaIYaGaamiEaaqaamaakaaabaGaci % 4yaiaac+gacaGG0bGaaGOmaiaadIhaaSqabaaaaaaa!4478! y' = \frac{{1 + {{\cot }^2}2x}}{{\sqrt {\cot 2x} }}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiabgkHiTmaabmaabaGaaGymaiabgUcaRiGa % cogacaGGVbGaaiiDamaaCaaaleqabaGaaGOmaaaakiaaikdacaWG4b % aacaGLOaGaayzkaaaabaWaaOaaaeaaciGGJbGaai4BaiaacshacaaI % YaGaamiEaaWcbeaaaaaaaa!46EE! y' = \frac{{ - \left( {1 + {{\cot }^2}2x} \right)}}{{\sqrt {\cot 2x} }}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaigdacqGHRaWkciGG0bGaaiyyaiaac6ga % daahaaWcbeqaaiaaikdaaaGccaaIYaGaamiEaaqaamaakaaabaGaci % 4yaiaac+gacaGG0bGaaGOmaiaadIhaaSqabaaaaaaa!4475! y' = \frac{{1 + {{\tan }^2}2x}}{{\sqrt {\cot 2x} }}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiabgkHiTmaabmaabaGaaGymaiabgUcaRiGa % cshacaGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaaikdacaWG4b % aacaGLOaGaayzkaaaabaWaaOaaaeaaciGGJbGaai4BaiaacshacaaI % YaGaamiEaaWcbeaaaaaaaa!46EA! y' = \frac{{ - \left( {1 + {{\tan }^2}2x} \right)}}{{\sqrt {\cot 2x} }}\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0IaaG % ymaiaaicdaciGGJbGaai4BaiaacohadaahaaWcbeqaaiaaisdaaaGc % caaIYaGaamiEaiaac6caaaa!3E89! - 10{\cos ^4}2x.\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaci % 4yaiaac+gacaGGZbWaaWbaaSqabeaacaaI0aaaaOGaaGOmaiaadIha % caGGUaGaci4CaiaacMgacaGGUbGaaGOmaiaadIhacaGGUaaaaa!4257! - {\cos ^4}2x.\sin 2x.\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0IaaG % ymaiaaicdaciGGJbGaai4BaiaacohadaahaaWcbeqaaiaaisdaaaGc % caaIYaGaamiEaiaac6caciGGZbGaaiyAaiaac6gacaWG4bGaaiOlaa % aa!4310! - 10{\cos ^4}2x.\sin x.\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0IaaG % ymaiaaicdaciGGJbGaai4BaiaacohadaahaaWcbeqaaiaaisdaaaGc % caaIYaGaamiEaiaac6caciGGZbGaaiyAaiaac6gacaaIYaGaamiEai % aac6caaaa!43CC! - 10{\cos ^4}2x.\sin 2x.\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4mamaabm % aabaGaci4CaiaacMgacaGGUbGaamiEaiabgUcaRiGacogacaGGVbGa % ai4CaiaadIhaaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaGcda % qadaqaaiGacogacaGGVbGaai4CaiaadIhacqGHRaWkciGGZbGaaiyA % aiaac6gacaWG4baacaGLOaGaayzkaaGaaiOlaaaa!4C76! 3{\left( {\sin x + \cos x} \right)^2}\left( {\cos x + \sin x} \right).\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4mamaabm % aabaGaci4CaiaacMgacaGGUbGaamiEaiabgkHiTiaadogacaGGVbGa % ai4CaiaadIhaaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaGcda % qadaqaaiGacogacaGGVbGaai4CaiaadIhacqGHsislciGGZbGaaiyA % aiaac6gacaWG4baacaGLOaGaayzkaaGaaiOlaaaa!4C8B! 3{\left( {\sin x - cosx} \right)^2}\left( {\cos x - \sin x} \right).\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaci % GGZbGaaiyAaiaac6gacaWG4bGaey4kaSIaci4yaiaac+gacaGGZbGa % amiEaaGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaakmaabmaaba % Gaci4yaiaac+gacaGGZbGaamiEaiabgkHiTiGacohacaGGPbGaaiOB % aiaadIhaaiaawIcacaGLPaaacaGGUaaaaa!4BC4! {\left( {\sin x + \cos x} \right)^2}\left( {\cos x - \sin x} \right).\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4mamaabm % aabaGaci4CaiaacMgacaGGUbGaamiEaiabgUcaRiGacogacaGGVbGa % ai4CaiaadIhaaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaGcda % qadaqaaiGacogacaGGVbGaai4CaiaadIhacqGHsislciGGZbGaaiyA % aiaac6gacaWG4baacaGLOaGaayzkaaGaaiOlaaaa!4C81! 3{\left( {\sin x + \cos x} \right)^2}\left( {\cos x - \sin x} \right).\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci % GGJbGaai4BaiaacohacaWG4bGaey4kaSIaaGOmaaqaaiaaikdadaGc % aaqaaiGacohacaGGPbGaaiOBaiaadIhacqGHRaWkcaaIYaGaamiEaa % WcbeaaaaGccaGGUaaaaa!4375! \frac{{\cos x + 2}}{{2\sqrt {\sin x + 2x} }}.\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci % GGJbGaai4BaiaacohacaWG4bGaey4kaSIaaGOmaaqaamaakaaabaGa % ci4CaiaacMgacaGGUbGaamiEaiabgUcaRiaaikdacaWG4baaleqaaa % aakiaac6caaaa!42B9! \frac{{\cos x + 2}}{{\sqrt {\sin x + 2x} }}.\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIYaaabaGaaGOmamaakaaabaGaci4CaiaacMgacaGGUbGaamiEaiab % gUcaRiaaikdacaWG4baaleqaaaaakiaac6caaaa!3EC3! \frac{2}{{2\sqrt {\sin x + 2x} }}.\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci % GGJbGaai4BaiaacohacaWG4baabaGaaGOmamaakaaabaGaci4Caiaa % cMgacaGGUbGaamiEaiabgUcaRiaaikdacaWG4baaleqaaaaakiaac6 % caaaa!41D7! \frac{{\cos x}}{{2\sqrt {\sin x + 2x} }}.\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ % gacaGGZbWaaOaaaeaacaaIYaGaey4kaSIaamiEamaaCaaaleqabaGa % aGOmaaaaaeqaaOGaaiOlaaaa!3D17! \cos \sqrt {2 + {x^2}} .\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaaabaWaaOaaaeaacaaIYaGaey4kaSIaamiEamaaCaaaleqabaGa % aGOmaaaaaeqaaaaakiaac6caciGGJbGaai4BaiaacohadaGcaaqaai % aaikdacqGHRaWkcaWG4bWaaWbaaSqabeaacaaIYaaaaaqabaGccaGG % Uaaaaa!4232! \frac{1}{{\sqrt {2 + {x^2}} }}.\cos \sqrt {2 + {x^2}} .\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaaabaGaaGOmaaaacaGGUaGaci4yaiaac+gacaGGZbWaaOaaaeaa % caaIYaGaey4kaSIaamiEamaaCaaaleqabaGaaGOmaaaaaeqaaOGaai % Olaaaa!3F50! \frac{1}{2}.\cos \sqrt {2 + {x^2}} .\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % WG4baabaWaaOaaaeaacaaIYaGaey4kaSIaamiEamaaCaaaleqabaGa % aGOmaaaaaeqaaaaakiaac6caciGGJbGaai4BaiaacohadaGcaaqaai % aaikdacqGHRaWkcaWG4bWaaWbaaSqabeaacaaIYaaaaaqabaGccaGG % Uaaaaa!4274! \frac{x}{{\sqrt {2 + {x^2}} }}.\cos \sqrt {2 + {x^2}} .\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiGacohacaGGPbGaaiOBamaalaaabaGaamiE % aaqaaiaaikdaaaaabaGaci4yaiaac+gacaGGZbWaaWbaaSqabeaaca % aIZaaaaOWaaSaaaeaacaWG4baabaGaaGOmaaaaaaaaaa!42E4! y' = \frac{{\sin \frac{x}{2}}}{{{{\cos }^3}\frac{x}{2}}}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaikdaciGGZbGaaiyAaiaac6gadaWcaaqa % aiaadIhaaeaacaaIYaaaaaqaaiGacogacaGGVbGaai4CamaaCaaale % qabaGaaG4maaaakmaalaaabaGaamiEaaqaaiaaikdaaaaaaaaa!43A0! y' = \frac{{2\sin \frac{x}{2}}}{{{{\cos }^3}\frac{x}{2}}}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiGacohacaGGPbGaaiOBamaalaaabaGaamiE % aaqaaiaaikdaaaaabaGaaGOmaiGacogacaGGVbGaai4CamaaCaaale % qabaGaaG4maaaakmaalaaabaGaamiEaaqaaiaaikdaaaaaaaaa!43A0! y' = \frac{{\sin \frac{x}{2}}}{{2{{\cos }^3}\frac{x}{2}}}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpciGG0bGaaiyyaiaac6gadaahaaWcbeqaaiaaiodaaaGc % daqadaqaamaalaaabaGaamiEaaqaaiaaikdaaaaacaGLOaGaayzkaa % aaaa!3FB9! y' = {\tan ^3}\left( {\frac{x}{2}} \right)\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaigdaaeaadaGcaaqaaiGacohacaGGPbGa % aiOBaiaadIhaaSqabaaaaOGaeyOeI0YaaSaaaeaacaaIXaaabaWaaO % aaaeaaciGGJbGaai4BaiaacohacaWG4baaleqaaaaaaaa!430B! y' = \frac{1}{{\sqrt {\sin x} }} - \frac{1}{{\sqrt {\cos x} }}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaigdaaeaadaGcaaqaaiGacohacaGGPbGa % aiOBaiaadIhaaSqabaaaaOGaey4kaSYaaSaaaeaacaaIXaaabaWaaO % aaaeaaciGGJbGaai4BaiaacohacaWG4baaleqaaaaaaaa!4300! y' = \frac{1}{{\sqrt {\sin x} }} + \frac{1}{{\sqrt {\cos x} }}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiGacogacaGGVbGaai4CaiaadIhaaeaadaGc % aaqaaiGacohacaGGPbGaaiOBaiaadIhaaSqabaaaaOGaeyOeI0YaaS % aaaeaaciGGZbGaaiyAaiaac6gacaWG4baabaWaaOaaaeaaciGGJbGa % ai4BaiaacohacaWG4baaleqaaaaaaaa!493A! y' = \frac{{\cos x}}{{\sqrt {\sin x} }} - \frac{{\sin x}}{{\sqrt {\cos x} }}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiGacogacaGGVbGaai4CaiaadIhaaeaadaGc % aaqaaiGacohacaGGPbGaaiOBaiaadIhaaSqabaaaaOGaey4kaSYaaS % aaaeaaciGGZbGaaiyAaiaac6gacaWG4baabaWaaOaaaeaaciGGJbGa % ai4BaiaacohacaWG4baaleqaaaaaaaa!492F! y' = \frac{{\cos x}}{{\sqrt {\sin x} }} + \frac{{\sin x}}{{\sqrt {\cos x} }}\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaGaci4yaiaac+gacaGGZbWaaOaaaeaacaWG4baa % leqaaaaa!3D4A! y' = 2\cos \sqrt x \)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaigdaaeaadaGcaaqaaiaadIhaaSqabaaa % aOGaci4yaiaac+gacaGGZbWaaOaaaeaacaWG4baaleqaaaaa!3E7B! y' = \frac{1}{{\sqrt x }}\cos \sqrt x \)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaWaaOaaaeaacaWG4baaleqaaOGaaiOlaiGacoga % caGGVbGaai4CamaalaaabaGaaGymaaqaamaakaaabaGaamiEaaWcbe % aaaaaaaa!3FE9! y' = 2\sqrt x .\cos \frac{1}{{\sqrt x }}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaigdaaeaadaGcaaqaaiaadIhaaSqabaGc % caGGUaGaci4yaiaac+gacaGGZbWaaOaaaeaacaWG4baaleqaaaaaaa % a!3F2D! y' = \frac{1}{{\sqrt x .\cos \sqrt x }}\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWdaNaey % 4kaSIaam4AaiaaikdacqaHapaCaaa!3BFC! \pi + k2\pi \)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWdaNaey % 4kaSIaam4AaiaaikdacqaHapaCaaa!3BFC! 2\pi + k4\pi \)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiabec % 8aWjabgUcaRiaadUgacqaHapaCaaa!3BFC! 2\pi + k\pi \)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiabec % 8aWjabgUcaRiaadUgacqaHapaCaaa!3BFC! \pi + k\pi \)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaWG4bWaaWbaaSqabeaacaaIYaaaaOGaaiOlaiGacohacaGG % PbGaaiOBaiaaikdacaWG4baabaGaaiikaiGacogacaGGVbGaai4Cai % aadIhacqGHRaWkcaWG4bGaci4CaiaacMgacaGGUbGaamiEaiaacMca % daahaaWcbeqaaiaaikdaaaaaaaaa!49EA! \frac{{ - {x^2}.\sin 2x}}{{{{(\cos x + x\sin x)}^2}}}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaWG4bWaaWbaaSqabeaacaaIYaaaaOGaaiOlaiGacohacaGG % PbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaadIhaaeaacaGGOaGaci % 4yaiaac+gacaGGZbGaamiEaiabgUcaRiaadIhaciGGZbGaaiyAaiaa % c6gacaWG4bGaaiykamaaCaaaleqabaGaaGOmaaaaaaaaaa!4A21! \frac{{ - {x^2}.{{\sin }^2}x}}{{{{(\cos x + x\sin x)}^2}}}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaWG4bWaaWbaaSqabeaacaaIYaaaaOGaaiOlaiGacogacaGG % VbGaai4CaiaaikdacaWG4baabaGaaiikaiGacogacaGGVbGaai4Cai % aadIhacqGHRaWkcaWG4bGaci4CaiaacMgacaGGUbGaamiEaiaacMca % daahaaWcbeqaaiaaikdaaaaaaaaa!49E5! \frac{{ - {x^2}.\cos 2x}}{{{{(\cos x + x\sin x)}^2}}}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaada % WcaaqaaiaadIhaaeaaciGGJbGaai4BaiaacohacaWG4bGaey4kaSIa % amiEaiGacohacaGGPbGaaiOBaiaadIhaaaaacaGLOaGaayzkaaWaaW % baaSqabeaacaaIYaaaaaaa!42F7! {\left( {\frac{x}{{\cos x + x\sin x}}} \right)^2}\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiabgkHiTiaaikdaciGGZbGaaiyAaiaac6ga % caaIYaGaamiEamaabmaabaGaaG4maiaadIhacqGHRaWkcaaIXaaaca % GLOaGaayzkaaGaeyOeI0IaaG4maiGacogacaGGVbGaai4Caiaaikda % caWG4baabaWaaeWaaeaacaaIZaGaamiEaiabgUcaRiaaigdaaiaawI % cacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaOGaaiOlaaaa!5087! y' = \frac{{ - 2\sin 2x\left( {3x + 1} \right) - 3\cos 2x}}{{{{\left( {3x + 1} \right)}^2}}}.\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiabgkHiTiaaikdaciGGZbGaaiyAaiaac6ga % caaIYaGaamiEamaabmaabaGaaG4maiaadIhacqGHRaWkcaaIXaaaca % GLOaGaayzkaaGaeyOeI0IaaG4maiGacogacaGGVbGaai4Caiaaikda % caWG4baabaGaaG4maiaadIhacqGHRaWkcaaIXaaaaiaac6caaaa!4E0B! y' = \frac{{ - 2\sin 2x\left( {3x + 1} \right) - 3\cos 2x}}{{3x + 1}}.\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiabgkHiTiGacohacaGGPbGaaiOBaiaaikda % caWG4bWaaeWaaeaacaaIZaGaamiEaiabgUcaRiaaigdaaiaawIcaca % GLPaaacqGHsislcaaIZaGaci4yaiaac+gacaGGZbGaaGOmaiaadIha % aeaadaqadaqaaiaaiodacaWG4bGaey4kaSIaaGymaaGaayjkaiaawM % caamaaCaaaleqabaGaaGOmaaaaaaGccaGGUaaaaa!4FCB! y' = \frac{{ - \sin 2x\left( {3x + 1} \right) - 3\cos 2x}}{{{{\left( {3x + 1} \right)}^2}}}.\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaaikdaciGGZbGaaiyAaiaac6gacaaIYaGa % amiEamaabmaabaGaaG4maiaadIhacqGHRaWkcaaIXaaacaGLOaGaay % zkaaGaey4kaSIaaG4maiGacogacaGGVbGaai4CaiaaikdacaWG4baa % baWaaeWaaeaacaaIZaGaamiEaiabgUcaRiaaigdaaiaawIcacaGLPa % aadaahaaWcbeqaaiaaikdaaaaaaOGaaiOlaaaa!4F8F! y' = \frac{{2\sin 2x\left( {3x + 1} \right) + 3\cos 2x}}{{{{\left( {3x + 1} \right)}^2}}}.\)

A. Cả hai đều sai 

B. Chỉ (I) 

C. Chỉ (II) 

D. Cả hai đều đúng

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG5bGbauaacqGH9aqpciGGJbGaai4BaiaacohacaWG4bGaeyOe % I0Iaci4CaiaacMgacaGGUbGaamiEaiabgUcaRiaaigdaaaa!4252! y' = \cos x - \sin x + 1\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0Jaci4yaiaac+gacaGGZbGaamiEaiabgUcaRiGacohacaGG % PbGaaiOBaiaadIhacqGHRaWkciGGJbGaai4BaiaacohacaaIYaGaam % iEaaaa!45F8! y' = \cos x + \sin x + \cos 2x\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG5bGbauaacqGH9aqpciGGJbGaai4BaiaacohacaWG4bGaeyOe % I0Iaci4CaiaacMgacaGGUbGaamiEaiabgUcaRiGacogacaGGVbGaai % 4CaiaaikdacaWG4baaaa!4623! y' = \cos x - \sin x + \cos 2x\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG5bGbauaacqGH9aqpciGGJbGaai4BaiaacohacaWG4bGaey4k % aSIaci4CaiaacMgacaGGUbGaamiEaiabgUcaRiaaigdaaaa!4247! y' = \cos x + \sin x + 1\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaGaamiEaiaac6caciGGJbGaai4BaiaacohacaWG % 4bGaeyOeI0IaamiEamaaCaaaleqabaGaaGOmaaaakiGacohacaGGPb % GaaiOBaiaadIhaaaa!4590! y' = 2x.\cos x - {x^2}\sin x\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaGaamiEaiaac6caciGGJbGaai4BaiaacohacaWG % 4bGaey4kaSIaamiEamaaCaaaleqabaGaaGOmaaaakiGacohacaGGPb % GaaiOBaiaadIhaaaa!4585! y' = 2x.\cos x + {x^2}\sin x\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaGaamiEaiaac6cacaGGZbGaaiyAaiaac6gacaWG % 4bGaeyOeI0IaamiEamaaCaaaleqabaGaaGOmaaaakiGacogacaGGVb % Gaai4CaiaadIhaaaa!458E! y' = 2x.sinx - {x^2}\cos x\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIYaGaamiEaiaac6caciGGZbGaaiyAaiaac6gacaWG % 4bGaey4kaSIaamiEamaaCaaaleqabaGaaGOmaaaakiGacogacaGGVb % Gaai4CaiaadIhaaaa!4585! y' = 2x.\sin x + {x^2}\cos x\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaadIhaciGGJbGaai4BaiaacohacaWG4bGa % ey4kaSIaci4CaiaacMgacaGGUbGaamiEaaqaaiaadIhadaahaaWcbe % qaaiaaikdaaaaaaaaa!441D! y' = \frac{{x\cos x + \sin x}}{{{x^2}}}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaadIhaciGGJbGaai4BaiaacohacaWG4bGa % eyOeI0Iaci4CaiaacMgacaGGUbGaamiEaaqaaiaadIhadaahaaWcbe % qaaiaaikdaaaaaaaaa!4428! y' = \frac{{x\cos x - \sin x}}{{{x^2}}}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaadIhaciGGZbGaaiyAaiaac6gacaWG4bGa % ey4kaSIaci4yaiaac+gacaGGZbGaamiEaaqaaiaadIhadaahaaWcbe % qaaiaaikdaaaaaaaaa!441D! y' = \frac{{x\sin x + \cos x}}{{{x^2}}}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaWcaaqaaiaadIhaciGGZbGaaiyAaiaac6gacaWG4bGa % eyOeI0Iaci4yaiaac+gacaGGZbGaamiEaaqaaiaadIhadaahaaWcbe % qaaiaaikdaaaaaaaaa!4428! y' = \frac{{x\sin x - \cos x}}{{{x^2}}}\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpciGGZbGaaiyAaiaac6gacaGG4bWaaeWaaeaacaaIZaGa % ci4yaiaac+gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGaamiEaiabgk % HiTiaaigdaaiaawIcacaGLPaaaaaa!4527! y' = {\mathop{\rm sinx}\nolimits} \left( {3{{\cos }^2}x - 1} \right)\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpciGGZbGaaiyAaiaac6gacaGG4bWaaeWaaeaacaaIZaGa % ci4yaiaac+gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGaamiEaiabgU % caRiaaigdaaiaawIcacaGLPaaaaaa!451C! y' = {\mathop{\rm sinx}\nolimits} \left( {3{{\cos }^2}x + 1} \right)\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpciGGZbGaaiyAaiaac6gacaGG4bWaaeWaaeaaciGGJbGa % ai4BaiaacohadaahaaWcbeqaaiaaikdaaaGccaWG4bGaey4kaSIaaG % ymaaGaayjkaiaawMcaaaaa!445F! y' = {\mathop{\rm sinx}\nolimits} \left( {{{\cos }^2}x + 1} \right)\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpciGGZbGaaiyAaiaac6gacaGG4bWaaeWaaeaaciGGJbGa % ai4BaiaacohadaahaaWcbeqaaiaaikdaaaGccaWG4bGaeyOeI0IaaG % ymaaGaayjkaiaawMcaaaaa!446A! y' = {\mathop{\rm sinx}\nolimits} \left( {{{\cos }^2}x - 1} \right)\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4CaiaacM % gacaGGUbWaaeWaaeaaciGG0bGaaiyyaiaac6gacaWG4baacaGLOaGa % ayzkaaGaeyyXIC9aaSaaaeaacaaIXaaabaGaci4yaiaac+gacaGGZb % WaaWbaaSqabeaacaaIYaaaaOGaamiEaaaacqGHflY1aaa!4845! \sin \left( {\tan x} \right) \cdot \frac{1}{{{{\cos }^2}x}} \cdot \)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaci % 4CaiaacMgacaGGUbWaaeWaaeaaciGG0bGaaiyyaiaac6gacaWG4baa % caGLOaGaayzkaaGaeyyXIC9aaSaaaeaacaaIXaaabaGaci4yaiaac+ % gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGaamiEaaaacqGHflY1aaa!4932! - \sin \left( {\tan x} \right) \cdot \frac{1}{{{{\cos }^2}x}} \cdot \)

C. \(sin(tanx)\)

D. \(-sin (tan x)\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaac6 % caciGGJbGaai4BaiaacohadaqadaqaamaalaaabaGaeqiWdahabaGa % aG4maaaacqGHsislcaWG4bWaaWbaaSqabeaacaaIYaaaaaGccaGLOa % Gaayzkaaaaaa!4166! x.\cos \left( {\frac{\pi }{3} - {x^2}} \right)\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaaabaGaaGOmaaaacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaci4y % aiaac+gacaGGZbWaaeWaaeaadaWcaaqaaiabec8aWbqaaiaaiodaaa % GaeyOeI0IaamiEaaGaayjkaiaawMcaaaaa!423B! \frac{1}{2}{x^2}\cos \left( {\frac{\pi }{3} - x} \right)\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaaabaGaaGOmaaaacaWG4bGaci4CaiaacMgacaGGUbWaaeWaaeaa % daWcaaqaaiabec8aWbqaaiaaiodaaaGaeyOeI0IaamiEaaGaayjkai % aawMcaaaaa!414D! \frac{1}{2}x\sin \left( {\frac{\pi }{3} - x} \right)\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaaabaGaaGOmaaaacaWG4bGaci4yaiaac+gacaGGZbWaaeWaaeaa % daWcaaqaaiabec8aWbqaaiaaiodaaaGaeyOeI0IaamiEamaaCaaale % qabaGaaGOmaaaaaOGaayjkaiaawMcaaaaa!423B! \frac{1}{2}x\cos \left( {\frac{\pi }{3} - {x^2}} \right)\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIZaGaci4yaiaac+gacaGGZbGaaG4maiaadIhaaeaadaGcaaqaaiGa % cohacaGGPbGaaiOBaiaaiodacaWG4baaleqaaaaakiabgwSixdaa!424E! \frac{{3\cos 3x}}{{\sqrt {\sin 3x} }} \cdot \)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIZaGaci4yaiaac+gacaGGZbGaaG4maiaadIhaaeaacaaIYaWaaOaa % aeaaciGGZbGaaiyAaiaac6gacaaIZaGaamiEaaWcbeaaaaGccqGHfl % Y1aaa!430A! \frac{{3\cos 3x}}{{2\sqrt {\sin 3x} }} \cdot \)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS % aaaeaacaaIZaGaci4yaiaac+gacaGGZbGaaG4maiaadIhaaeaacaaI % YaWaaOaaaeaaciGGZbGaaiyAaiaac6gacaaIZaGaamiEaaWcbeaaaa % GccqGHflY1aaa!43F7! - \frac{{3\cos 3x}}{{2\sqrt {\sin 3x} }} \cdot \)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaci % GGJbGaai4BaiaacohacaaIZaGaamiEaaqaaiaaikdadaGcaaqaaiGa % cohacaGGPbGaaiOBaiaaiodacaWG4baaleqaaaaakiabgwSixdaa!424D! \frac{{\cos 3x}}{{2\sqrt {\sin 3x} }} \cdot \)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGinaiGaco % gacaGGVbGaai4CaiaaikdacaWG4bGaey4kaSIaaGOmaiGacohacaGG % PbGaaiOBaiaaikdacaWG4baaaa!416C! 4\cos 2x + 2\sin 2x\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiGaco % gacaGGVbGaai4CaiaaikdacaWG4bGaeyOeI0IaaGOmaiGacohacaGG % PbGaaiOBaiaaikdacaWG4baaaa!4175! 2\cos 2x - 2\sin 2x\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGinaiGaco % gacaGGVbGaai4CaiaaikdacaWG4bGaey4kaSIaaGOmaiGacohacaGG % PbGaaiOBaiaaikdacaWG4baaaa!416C! 4\cos 2x - 2\sin 2x\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0IaaG % inaiGacogacaGGVbGaai4CaiaaikdacaWG4bGaeyOeI0IaaGOmaiGa % cohacaGGPbGaaiOBaiaaikdacaWG4baaaa!4264! - 4\cos 2x - 2\sin 2x\)

A. -2sin2x

B. 2sin2x

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaci % 4yaiaac+gacaGGZbWaaeWaaeaadaWcaaqaaiabec8aWbqaaiaaikda % aaGaeyOeI0IaaGOmaiaadIhaaiaawIcacaGLPaaaaaa!406B! - \cos \left( {\frac{\pi }{2} - 2x} \right)\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaci % 4yaiaac+gacaGGZbWaaeWaaeaadaWcaaqaaiabec8aWbqaaiaaikda % aaGaeyOeI0IaaGOmaiaadIhaaiaawIcacaGLPaaaaaa!406B! \cos \left( {\frac{\pi }{2} - 2x} \right)\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aI3aaabaGaci4yaiaac+gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGa % aG4naiaadIhaaaaaaa!3C48! \frac{7}{{{{\cos }^2}7x}}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS % aaaeaacaaI3aaabaGaci4yaiaac+gacaGGZbWaaWbaaSqabeaacaaI % YaaaaOGaaG4naiaadIhaaaaaaa!3D35! - \frac{7}{{{{\cos }^2}7x}}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS % aaaeaacaaI3aaabaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaI % YaaaaOGaaG4naiaadIhaaaaaaa!3D3A! - \frac{7}{{{{\sin }^2}7x}}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aI3aGaamiEaaqaaiGacogacaGGVbGaai4CamaaCaaaleqabaGaaGOm % aaaakiaaiEdacaWG4baaaaaa!3D45! \frac{{7x}}{{{{\cos }^2}7x}}\)

A. \(y' = 1 + tanx\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaqadaqaaiaaigdacqGHRaWkciGG0bGaaiyyaiaac6ga % caWG4baacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaaa!407F! y' = {\left( {1 + \tan x} \right)^2}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaqadaqaaiaaigdacqGHRaWkciGG0bGaaiyyaiaac6ga % caWG4baacaGLOaGaayzkaaWaaeWaaeaacaaIXaGaey4kaSIaciiDai % aacggacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaamiEaaGaayjkaiaa % wMcaaaaa!477D! y' = \left( {1 + \tan x} \right)\left( {1 + {{\tan }^2}x} \right)\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIXaGaey4kaSIaciiDaiaacggacaGGUbWaaWbaaSqa % beaacaaIYaaaaOGaamiEaaaa!3F00! y' = 1 + {\tan ^2}x\)

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaWG4baabaGaaGOmaiGacohacaGGPbGaaiOBaiaadIhadaah % aaWcbeqaaiaaikdaaaaaaOGaeyyXICnaaa!3FBC! \frac{{ - x}}{{2\sin {x^2}}} \cdot \)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % WG4baabaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOGa % amiEamaaCaaaleqabaGaaGOmaaaaaaGccqGHflY1aaa!3F06! \frac{x}{{{{\sin }^2}{x^2}}} \cdot \)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaWG4baabaGaci4CaiaacMgacaGGUbGaamiEamaaCaaaleqa % baGaaGOmaaaaaaGccqGHflY1aaa!3F00! \frac{{ - x}}{{\sin {x^2}}} \cdot \)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHsislcaWG4baabaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaI % YaaaaOGaamiEamaaCaaaleqabaGaaGOmaaaaaaGccqGHflY1aaa!3FF3! \frac{{ - x}}{{{{\sin }^2}{x^2}}} \cdot \)