derivative f(x)=-8/(x^3)

解答

导数

f (x) = - \frac{8}{x ^{3}}

\frac{24}{x ^{4}}

求解步骤

\frac{d}{d x} (- \frac{8}{x ^{3}})

将常数提出:

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

= - 8 \frac{d}{d x} (\frac{1}{x ^{3}})

使用指数法则:

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

= - 8 \frac{d}{d x} (x^{- 3})

使用幂法则:

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

= - 8 (- 3 x^{- 3 - 1})

化简

- 8 (- 3 x^{- 3 - 1}) : \frac{24}{x ^{4}}

= \frac{24}{x ^{4}}

\frac{d y}{d x} = x y

d er i v a t i v e f (x) = \frac{4}{3} π x^{2}

\frac{\partial}{\partial y} ((x - y)^{2} y)

\frac{\partial}{\partial x} (3 arctan (\frac{x}{y}))

y^{^{''}} - 8 y^{^{'}} + 15 y = - sin (2 t)