Tính đạo hàm của hàm số sau: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9maabmaabaWaaSaaaeaaciGGZbGaaiyAaiaac6gacaWG4baabaGa % aGymaiabgUcaRiGacogacaGGVbGaai4CaiaadIhaaaaacaGLOaGaay % zkaaWaaWbaaSqabeaacaaIZaaaaaaa!43BD! y = {\left( {\frac{{\sin x}}{{1 + \cos x}}} \right)^3}\)

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

Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án

Môn: Toán Lớp 11

Chủ đề: Hàm số lượng giác và phương trình lượng giác

Bài: Phương trình lượng giác cơ bản

Lời giải:

Báo sai

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIZaWaaeWaaeaadaWcaaqaaiGacohacaGGPbGaaiOB % aiaadIhaaeaacaaIXaGaey4kaSIaci4yaiaac+gacaGGZbGaamiEaa % aaaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaGccaGGUaWaaeWa % aeaadaWcaaqaaiGacohacaGGPbGaaiOBaaqaaiaaigdacqGHRaWkci % GGJbGaai4BaiaacohacaWG4baaaaGaayjkaiaawMcaamaaCaaaleqa % baGaai4laaaaaaa!509E! y' = 3{\left( {\frac{{\sin x}}{{1 + \cos x}}} \right)^2}.{\left( {\frac{{\sin }}{{1 + \cos x}}} \right)^/}\)

Tính \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaada % WcaaqaaiGacohacaGGPbGaaiOBaiaadIhaaeaacaaIXaGaey4kaSIa % ci4yaiaac+gacaGGZbGaamiEaaaaaiaawIcacaGLPaaadaahaaWcbe % qaaiaac+caaaGccqGH9aqpdaWcaaqaamaabmaabaGaci4CaiaacMga % caGGUbGaamiEaaGaayjkaiaawMcaamaaCaaaleqabaGaai4laaaakm % aabmaabaGaaGymaiabgUcaRiGacogacaGGVbGaai4CaiaadIhaaiaa % wIcacaGLPaaacqGHsisldaqadaqaaiaaigdacqGHRaWkciGGJbGaai % 4BaiaacohacaWG4baacaGLOaGaayzkaaWaaWbaaSqabeaacaGGVaaa % aOGaaiOlaiGacohacaGGPbGaaiOBaiaadIhaaeaadaqadaqaaiaaig % dacqGHRaWkciGGJbGaai4BaiaacohacaWG4baacaGLOaGaayzkaaWa % aWbaaSqabeaacaaIYaaaaaaakiabg2da9maalaaabaGaci4yaiaac+ % gacaGGZbGaamiEamaabmaabaGaaGymaiabgUcaRiGacogacaGGVbGa % ai4CaiaadIhaaiaawIcacaGLPaaacqGHRaWkciGGZbGaaiyAaiaac6 % gadaahaaWcbeqaaiaaikdaaaGccaWG4baabaWaaeWaaeaacaaIXaGa % ey4kaSIaci4yaiaac+gacaGGZbGaamiEaaGaayjkaiaawMcaamaaCa % aaleqabaGaaGOmaaaaaaaaaa!7EAF! {\left( {\frac{{\sin x}}{{1 + \cos x}}} \right)^/} = \frac{{{{\left( {\sin x} \right)}^/}\left( {1 + \cos x} \right) - {{\left( {1 + \cos x} \right)}^/}.\sin x}}{{{{\left( {1 + \cos x} \right)}^2}}} = \frac{{\cos x\left( {1 + \cos x} \right) + {{\sin }^2}x}}{{{{\left( {1 + \cos x} \right)}^2}}}\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS % aaaeaaciGGJbGaai4BaiaacohacaWG4bGaey4kaSIaci4yaiaac+ga % caGGZbWaaWbaaSqabeaacaaIYaaaaOGaamiEaiabgUcaRiGacohaca % GGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaadIhaaeaadaqadaqa % aiaaigdacqGHRaWkciGGJbGaai4BaiaacohacaWG4baacaGLOaGaay % zkaaWaaWbaaSqabeaacaaIYaaaaaaakiabg2da9maalaaabaGaaGym % aaqaaiaaigdacqGHRaWkciGGJbGaai4BaiaacohacaWG4baaaaaa!5550! = \frac{{\cos x + {{\cos }^2}x + {{\sin }^2}x}}{{{{\left( {1 + \cos x} \right)}^2}}} = \frac{1}{{1 + \cos x}}\)

Vậy \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIZaWaaeWaaeaadaWcaaqaaiGacohacaGGPbGaaiOB % aiaadIhaaeaacaaIXaGaey4kaSIaci4yaiaac+gacaGGZbGaamiEaa % aaaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaGccaGGUaWaaSaa % aeaacaaIXaaabaGaaGymaiabgUcaRiGacogacaGGVbGaai4CaiaadI % haaaGaeyypa0ZaaSaaaeaacaaIZaGaci4CaiaacMgacaGGUbWaaWba % aSqabeaacaaIYaaaaOGaamiEaaqaamaabmaabaGaaGymaiabgUcaRi % GacogacaGGVbGaai4CaiaadIhaaiaawIcacaGLPaaadaahaaWcbeqa % aiaaiodaaaaaaaaa!5A93! y' = 3{\left( {\frac{{\sin x}}{{1 + \cos x}}} \right)^2}.\frac{1}{{1 + \cos x}} = \frac{{3{{\sin }^2}x}}{{{{\left( {1 + \cos x} \right)}^3}}}\)