derivative of 1/(2\sqrt[3]{x^2})

解答

\frac{d}{d x} (\frac{1}{2 3 x ^{2}})

- \frac{1}{3 x ^{\frac{5}{3}}}

求解步骤

\frac{d}{d x} (\frac{1}{2 3 x ^{2}})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d x} (\frac{1}{3 x ^{2}})

使用指数法则:

\frac{1}{a} = a^{- 1}

= \frac{1}{2} \frac{d}{d x} ((x^{2})^{- \frac{1}{3}})

使用连锁律:

- \frac{1}{3 ( x ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} (x^{2})

= - \frac{1}{3 ( x ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} (x^{2})

\frac{d}{d x} (x^{2}) = 2 x

= \frac{1}{2} (- \frac{1}{3 ( x ^{2} ) ^{\frac{4}{3}}} \cdot 2 x)

化简

\frac{1}{2} (- \frac{1}{3 ( x ^{2} ) ^{\frac{4}{3}}} \cdot 2 x) : - \frac{1}{3 x ^{\frac{5}{3}}}

= - \frac{1}{3 x ^{\frac{5}{3}}}

\int_{0}^{\infty} sin (4 x) d x

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a re a e^{x}, x e^{x^{2}}, [0, 1]