derivative 1/(4s^3)

解答

导数

\frac{1}{4 s ^{3}}

- \frac{3}{4 s ^{4}}

求解步骤

\frac{d}{d s} (\frac{1}{4 s ^{3}})

将常数提出:

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

= \frac{1}{4} \frac{d}{d s} (\frac{1}{s ^{3}})

使用指数法则:

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

= \frac{1}{4} \frac{d}{d s} (s^{- 3})

使用幂法则:

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

= \frac{1}{4} (- 3 s^{- 3 - 1})

化简

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

= - \frac{3}{4 s ^{4}}

\frac{\partial}{\partial x} (1 - x^{2} - x - 3 y^{2} + y)

\frac{\partial}{\partial x} (x y - 4 x^{2} y)

y^{^{'}} = 4 y + x^{2} + 9

\int (3^{x} - sec^{2} (x)) d x

\frac{d y}{d x} = - 4 x + 6 x^{2}