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

解答

导数

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

\frac{2 x ^{2} - 6 x + 2}{( 2 x - 3 ) ^{2}}

求解步骤

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

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

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

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

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

乘开

2 x (2 x - 3) - 2 (x^{2} - 1) : 2 x^{2} - 6 x + 2

= \frac{2 x ^{2} - 6 x + 2}{( 2 x - 3 ) ^{2}}

\frac{\partial}{\partial y} (4 x^{3} y^{3} + 3)

\frac{d}{d x} (4 x + 5)

\int sin^{3} (4 x) cos^{- 2} (4 x) d x

\int cot^{7} (\frac{x}{2}) csc^{2} (\frac{x}{2}) d x

s l o p e (- 2, - 9), (0, - 3)