derivative of 1/(x^{1/3})

解答

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

- \frac{1}{3 x ^{\frac{4}{3}}}

求解步骤

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

使用指数法则:

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

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

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

化简

- \frac{1}{3} x^{- \frac{1}{3} - 1} : - \frac{1}{3 x ^{\frac{4}{3}}}

= - \frac{1}{3 x ^{\frac{4}{3}}}