Tính đạo hàm của hàm số sau \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI % cacaWG4bGaaiykaiabg2da9maaceaaeaqabeaacaWG4bWaaWbaaSqa % beaacaaIZaaaaOGaci4CaiaacMgacaGGUbWaaSaaaeaacaaIXaaaba % GaamiEaaaacaqGGaGaaeiiaiaabUgacaqGObGaaeyAaiaabccacaWG % 4bGaeyiyIKRaaGimaaqaaiaaicdacaqGGaGaaeiiaiaabccacaqGGa % GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae4AaiaabIga % caqGPbGaaeiiaiaadIhacqGH9aqpcaaIWaGaaeiiaaaacaGL7baaaa % a!57F9! f(x) = \left\{ \begin{array}{l} {x^3}\sin \frac{1}{x}{\rm{ khi }}x \ne 0\\ 0{\rm{ khi }}x = 0{\rm{ }} \end{array} \right.\)
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Lời giải:
Báo sai\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabgc % Mi5kaaicdacqGHshI3caWGMbGaai4jaiaacIcacaWG4bGaaiykaiab % g2da9iaaiodacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaci4CaiaacM % gacaGGUbWaaSaaaeaacaaIXaaabaGaamiEaaaacqGHsislcaWG4bGa % ci4yaiaac+gacaGGZbWaaSaaaeaacaaIXaaabaGaamiEaaaaaaa!4E93! x \ne 0 \Rightarrow f'(x) = 3{x^2}\sin \frac{1}{x} - x\cos \frac{1}{x}\)
Với \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 % da9iaaicdacqGHshI3caWGMbGaai4jaiaacIcacaaIWaGaaiykaiab % g2da9maaxababaGaciiBaiaacMgacaGGTbaaleaacaWG4bGaeyOKH4 % QaaGimaaqabaGcdaWcaaqaaiaadAgacaGGOaGaamiEaiaacMcacqGH % sislcaWGMbGaaiikaiaaicdacaGGPaaabaGaamiEaaaacqGH9aqpca % aIWaaaaa!506D! x = 0 \Rightarrow f'(0) = \mathop {\lim }\limits_{x \to 0} \frac{{f(x) - f(0)}}{x} = 0\)
Vậy \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE % cacaGGOaGaamiEaiaacMcacqGH9aqpdaGabaabaeqabaGaaG4maiaa % dIhadaahaaWcbeqaaiaaikdaaaGcciGGZbGaaiyAaiaac6gadaWcaa % qaaiaaigdaaeaacaWG4baaaiabgkHiTiaadIhaciGGJbGaai4Baiaa % cohadaWcaaqaaiaaigdaaeaacaWG4baaaiaabccacaqGGaGaaeiiai % aabUgacaqGObGaaeyAaiaabccacaWG4bGaeyiyIKRaaGimaaqaaiaa % icdacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabUgacaqGObGaae % yAaiaabccacaqGGaGaaeiiaiaadIhacqGH9aqpcaaIWaaaaiaawUha % aaaa!5DFC! f'(x) = \left\{ \begin{array}{l} 3{x^2}\sin \frac{1}{x} - x\cos \frac{1}{x}{\rm{ khi }}x \ne 0\\ 0{\rm{ khi }}x = 0 \end{array} \right.\)