derivative (2x-3)/(4x+1)

解答

导数

\frac{2 x - 3}{4 x + 1}

\frac{14}{( 4 x + 1 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{2 x - 3}{4 x + 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} ( 2 x - 3 ) ( 4 x + 1 ) - \frac{d}{d x} ( 4 x + 1 ) ( 2 x - 3 )}{( 4 x + 1 ) ^{2}}

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

\frac{d}{d x} (4 x + 1) = 4

= \frac{2 ( 4 x + 1 ) - 4 ( 2 x - 3 )}{( 4 x + 1 ) ^{2}}

乘开

2 (4 x + 1) - 4 (2 x - 3) : 14

= \frac{14}{( 4 x + 1 ) ^{2}}

\int (3 x - 1) x + 6 d x

d er i v a t i v e ln (\frac{2 x + 1}{x ^{2} - 4})

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

x \to 0 + lim ((1 + 4 x)^{c o t (x)})

t a y l or x^{2} + 1