derivative-5/(x^6)

解答

导数

- \frac{5}{x ^{6}}

\frac{30}{x ^{7}}

求解步骤

\frac{d}{d x} (- \frac{5}{x ^{6}})

将常数提出:

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

= - 5 \frac{d}{d x} (\frac{1}{x ^{6}})

使用指数法则:

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

= - 5 \frac{d}{d x} (x^{- 6})

使用幂法则:

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

= - 5 (- 6 x^{- 6 - 1})

化简

- 5 (- 6 x^{- 6 - 1}) : \frac{30}{x ^{7}}

= \frac{30}{x ^{7}}

d er i v a t i v e ln (2^{x})

\int \frac{t ^{2}}{1 + t ^{2}} d t

\int 8 x^{3} + \frac{1}{x} d x

\frac{\partial}{\partial y} (e^{7 x e^{y}})

d er i v a t i v e f (x) = 6 x^{3} cot (x)