derivative of (3x-8/(x^2-1))

解答

\frac{d}{d x} (\frac{3 x - 8}{x ^{2} - 1})

\frac{- 3 x ^{2} + 16 x - 3}{( x ^{2} - 1 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{3 x - 8}{x ^{2} - 1})

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} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) ( 3 x - 8 )}{( x ^{2} - 1 ) ^{2}}

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

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

= \frac{3 ( x ^{2} - 1 ) - 2 x ( 3 x - 8 )}{( x ^{2} - 1 ) ^{2}}

乘开

3 (x^{2} - 1) - 2 x (3 x - 8) : - 3 x^{2} + 16 x - 3

= \frac{- 3 x ^{2} + 16 x - 3}{( x ^{2} - 1 ) ^{2}}

d er i v a t i v e y = \frac{9}{x ^{- 6}}

in v erse l a pl a ce {\frac{s}{( s - 2 ) ( s - 3 ) ( s - 6 )}}

\frac{d}{d x} ((x + a) e^{3 x} + b)

d er i v a t i v e 4 x^{- 3} + 6 x^{- \frac{8}{3}}

\frac{\partial}{\partial x} (arcsin (3 x + y))