derivative f(x)=-2/(x^2)

解答

导数

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

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

求解步骤

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

将常数提出:

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

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

使用指数法则:

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

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

使用幂法则:

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

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

化简

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

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

t an g e n t f (x) = x^{3} + 6 x^{2} + 19 x + 15, at x = 7

d er i v a t i v e y = 10 x

\frac{d}{d x} (6 e^{x} + \frac{2}{3 x})

(3 t^{2})^{^{'}}

im pl i c i t \frac{d y}{d x}, y = 4^{x}