Hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9maalaaabaGaci4CaiaacMgacaGGUbGaamiEaiabgkHiTiaadIha % ciGGJbGaai4BaiaacohacaWG4baabaGaci4yaiaac+gacaGGZbGaam % iEaiabgUcaRiaadIhaciGGZbGaaiyAaiaac6gacaWG4baaaaaa!4B1B! y = \frac{{\sin x - x\cos x}}{{\cos x + x\sin x}}\) có đạo hàm bằng

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

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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-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaaceWG5b % GbauaacqGH9aqpdaWcaaqaamaabmaabaGaci4CaiaabMgacaqGUbGa % amiEaiabgkHiTiaadIhaciGGJbGaai4BaiaacohacaWG4baacaGLOa % GaayzkaaWaaWbaaSqabeaakiadacUHYaIOaaWaaeWaaeaaciGGJbGa % ai4BaiaacohacaWG4bGaey4kaSIaamiEaiGacohacaGGPbGaaiOBai % aadIhaaiaawIcacaGLPaaacqGHsisldaqadaqaaiGacogacaGGVbGa % ai4CaiaadIhacqGHRaWkcaWG4bGaci4CaiaacMgacaGGUbGaamiEaa % GaayjkaiaawMcaamaaCaaaleqabaGccWaGGBOmGikaamaabmaabaGa % ci4CaiaabMgacaqGUbGaamiEaiabgkHiTiaadIhaciGGJbGaai4Bai % aacohacaWG4baacaGLOaGaayzkaaaabaWaaeWaaeaaciGGJbGaai4B % aiaacohacaWG4bGaey4kaSIaamiEaiGacohacaGGPbGaaiOBaiaadI % haaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaaGcbaGaaGPa % VlaaykW7caaMc8UaaGPaVlaaykW7cqGH9aqpdaWcaaqaaiaadIhaci % GGZbGaaiyAaiaac6gacaWG4bWaaeWaaeaaciGGJbGaai4Baiaacoha % caWG4bGaey4kaSIaamiEaiGacohacaGGPbGaaiOBaiaadIhaaiaawI % cacaGLPaaacqGHsislcaWG4bGaci4yaiaac+gacaGGZbGaamiEamaa % bmaabaGaci4CaiaabMgacaqGUbGaamiEaiabgkHiTiaadIhaciGGJb % Gaai4BaiaacohacaWG4baacaGLOaGaayzkaaaabaWaaeWaaeaaciGG % JbGaai4BaiaacohacaWG4bGaey4kaSIaamiEaiGacohacaGGPbGaai % OBaiaadIhaaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaOGa % eyypa0ZaaeWaaeaadaWcaaqaaiaadIhaaeaaciGGJbGaai4Baiaaco % hacaWG4bGaey4kaSIaamiEaiGacohacaGGPbGaaiOBaiaadIhaaaaa % caGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaaaaa!BB11! \begin{array}{l} y' = \frac{{{{\left( {{\mathop{\rm s}\nolimits} {\rm{in}}x - x\cos x} \right)}^\prime }\left( {\cos x + x\sin x} \right) - {{\left( {\cos x + x\sin x} \right)}^\prime }\left( {{\mathop{\rm s}\nolimits} {\rm{in}}x - x\cos x} \right)}}{{{{\left( {\cos x + x\sin x} \right)}^2}}}\\ \,\,\,\,\, = \frac{{x\sin x\left( {\cos x + x\sin x} \right) - x\cos x\left( {{\mathop{\rm s}\nolimits} {\rm{in}}x - x\cos x} \right)}}{{{{\left( {\cos x + x\sin x} \right)}^2}}} = {\left( {\frac{x}{{\cos x + x\sin x}}} \right)^2} \end{array}\)