Cho hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaabm % aabaGaamiEaaGaayjkaiaawMcaaiaaykW7cqGH9aqpdaGcbaqaaiaa % dIhaaSqaaiaaiodaaaaaaa!3DCA! f\left( x \right)\, = \sqrt[3]{x}\). Giá trị f’(8)bằng:
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Lời giải:
Báo saiVới x > 0
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaCa % aaleqabaGccWaGGBOmGikaamaabmaabaGaamiEaaGaayjkaiaawMca % aiaaykW7cqGH9aqpdaqadaqaaiaadIhadaahaaWcbeqaamaalaaaba % GaaGymaaqaaiaaiodaaaaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaa % kiadacUHYaIOaaGaeyypa0ZaaSaaaeaacaaIXaaabaGaaG4maaaaca % WG4bWaaWbaaSqabeaadaWcaaqaaiabgkHiTiaaikdaaeaacaaIZaaa % aaaakiabgkDiElaadAgadaahaaWcbeqaaOGamai4gkdiIcaadaqada % qaaiaaiIdaaiaawIcacaGLPaaacqGH9aqpdaWcaaqaaiaaigdaaeaa % caaIZaaaaiaac6cacaaI4aWaaWbaaSqabeaadaWcaaqaaiabgkHiTi % aaikdaaeaacaaIZaaaaaaakiabg2da9maalaaabaGaaGymaaqaaiaa % iodaaaGaaGOmamaaCaaaleqabaGaeyOeI0IaaGOmaaaakiabg2da9m % aalaaabaGaaGymaaqaaiaaigdacaaIYaaaaaaa!6483! {f^\prime }\left( x \right)\, = {\left( {{x^{\frac{1}{3}}}} \right)^\prime } = \frac{1}{3}{x^{\frac{{ - 2}}{3}}} \Rightarrow {f^\prime }\left( 8 \right) = \frac{1}{3}{.8^{\frac{{ - 2}}{3}}} = \frac{1}{3}{2^{ - 2}} = \frac{1}{{12}}\)