derivative F(r)= 2/(r^3)

解答

导数

F (r) = \frac{2}{r ^{3}}

- \frac{6}{r ^{4}}

求解步骤

\frac{d}{d r} (\frac{2}{r ^{3}})

将常数提出:

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

= 2 \frac{d}{d r} (\frac{1}{r ^{3}})

使用指数法则:

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

= 2 \frac{d}{d r} (r^{- 3})

使用幂法则:

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

= 2 (- 3 r^{- 3 - 1})

化简

2 (- 3 r^{- 3 - 1}) : - \frac{6}{r ^{4}}

= - \frac{6}{r ^{4}}

\frac{\partial}{\partial x} (\frac{6}{5} - \frac{6}{5} e^{- 20 t})

\frac{d}{d t} (2 cos (3 t))

\int_{0}^{\frac{9}{10}} \frac{1}{( 100 x ^{2} + 1 ) ^{\frac{3}{2}}} d x

12 x^{3} - 3 y^{2} x^{4} + 1 \cdot y^{^{'}} = 0

\int \frac{1}{( x ^{2} - 49 ) ^{2}} d x