derivative y=-1/(x^2)

解答

导数

y = - \frac{1}{x ^{2}}

\frac{2}{x ^{3}}

求解步骤

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

将常数提出:

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

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

使用指数法则:

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

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

使用幂法则:

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

= - (- 2 x^{- 2 - 1})

化简

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

= \frac{2}{x ^{3}}

\frac{d}{d x} (x^{7} e^{4 x})

\int x^{5} sin (x^{6}) d x

\frac{d}{d x} \frac{3}{( ( 56 ) ( 2 x - 1 ) ^{7} )} - \frac{1}{( ( 24 ) ( 2 x - 1 ) ^{6} )} - \frac{1}{( ( 40 ( 2 x - 1 ) ^{5} ) )}

\frac{d}{d x} (\frac{1}{x + y ^{2}})

y^{^{'}} = 2 x + 3 y - 1