Cho hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9maalaaabaGaaGymaiabgUcaRiGacohacaGGPbGaaiOBaiaadIha % aeaacaaIXaGaey4kaSIaci4yaiaac+gacaGGZbGaamiEaaaaaaa!42E6! y = \frac{{1 + \sin x}}{{1 + \cos x}}\). Xét hai kết quả:
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0ZaaSaaaeaadaqadaqaaiGacogacaGGVbGaai4CaiaadIha % cqGHsislciGGZbGaaiyAaiaac6gacaWG4baacaGLOaGaayzkaaWaae % WaaeaacaaIXaGaey4kaSIaci4yaiaac+gacaGGZbGaamiEaiabgUca % RiGacohacaGGPbGaaiOBaiaadIhaaiaawIcacaGLPaaaaeaadaqada % qaaiaaigdacqGHRaWkciGGJbGaai4BaiaacohacaWG4baacaGLOaGa % ayzkaaWaaWbaaSqabeaacaaIYaaaaaaaaaa!55BA! (I) y' = \frac{{\left( {\cos x - \sin x} \right)\left( {1 + \cos x + \sin x} \right)}}{{{{\left( {1 + \cos x} \right)}^2}}}\)
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0ZaaSaaaeaacaaIXaGaey4kaSIaci4yaiaac+gacaGGZbGa % amiEaiabgUcaRiGacohacaGGPbGaaiOBaiaadIhaaeaadaqadaqaai % aaigdacqGHRaWkciGGJbGaai4BaiaacohacaWG4baacaGLOaGaayzk % aaWaaWbaaSqabeaacaaIYaaaaaaaaaa!4A16! (II)y' = \frac{{1 + \cos x + \sin x}}{{{{\left( {1 + \cos x} \right)}^2}}}\)
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Lời giải:
Báo sai\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0ZaaSaaaeaaciGGJbGaai4BaiaacohacaWG4bGaaiikaiaa % igdacqGHRaWkciGGJbGaai4BaiaacohacaWG4bGaaiykaiabgUcaRi % GacohacaqGPbGaaeOBaiaadIhacaGGOaGaaGymaiabgUcaRiGacoha % caqGPbGaaeOBaiaadIhacaGGPaaabaWaaeWaaeaacaaIXaGaey4kaS % Iaci4yaiaac+gacaGGZbGaamiEaaGaayjkaiaawMcaamaaCaaaleqa % baGaaGOmaaaaaaGccqGH9aqpdaWcaaqaaiaaigdacqGHRaWkciGGZb % GaaeyAaiaab6gacaWG4bGaey4kaSIaci4yaiaac+gacaGGZbGaamiE % aaqaamaabmaabaGaaGymaiabgUcaRiGacogacaGGVbGaai4CaiaadI % haaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaaaa!6928! y' = \frac{{\cos x(1 + \cos x) + {\mathop{\rm s}\nolimits} {\rm{in}}x(1 + {\mathop{\rm s}\nolimits} {\rm{in}}x)}}{{{{\left( {1 + \cos x} \right)}^2}}} = \frac{{1 + {\mathop{\rm s}\nolimits} {\rm{in}}x + \cos x}}{{{{\left( {1 + \cos x} \right)}^2}}}\)
