derivative (3x+8)/(x^2)

解答

导数

\frac{3 x + 8}{x ^{2}}

\frac{- 3 x - 16}{x ^{3}}

求解步骤

\frac{d}{d x} (\frac{3 x + 8}{x ^{2}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 3 x + 8 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 3 x + 8 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (3 x + 8) = 3

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

= \frac{3 x ^{2} - 2 x ( 3 x + 8 )}{( x ^{2} ) ^{2}}

化简

\frac{3 x ^{2} - 2 x ( 3 x + 8 )}{( x ^{2} ) ^{2}} : \frac{- 3 x - 16}{x ^{3}}

= \frac{- 3 x - 16}{x ^{3}}

in v erse l a pl a ce \frac{( 3 s + 1 )}{s + 2}

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

\int_{1}^{3} (x^{3} + \frac{1}{4 x ^{3}}) d x

n or ma l y = 2 x - 1 + 4 x^{2}, (1, 5)

\int k e^{- x} d x