derivative y=(2x+1)/(2x-1)

解答

导数

y = \frac{2 x + 1}{2 x - 1}

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

求解步骤

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

\frac{d}{d x} (2 x + 1) = 2

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

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

化简

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

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