derivative of (-1/(x^3))

解答

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

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

求解步骤

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

化简

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

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

将常数提出:

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

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

使用指数法则:

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

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

使用幂法则:

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

= - (- 3 x^{- 3 - 1})

化简

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

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