derivative f(x)=(4x+3)/(4x-3)

解

導関数

f (x) = \frac{4 x + 3}{4 x - 3}

- \frac{24}{( 4 x - 3 ) ^{2}}

解答ステップ

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

商の法則を適用:

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

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

\frac{d}{d x} (4 x + 3) = 4

\frac{d}{d x} (4 x - 3) = 4

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

簡素化

\frac{4 ( 4 x - 3 ) - 4 ( 4 x + 3 )}{( 4 x - 3 ) ^{2}} : - \frac{24}{( 4 x - 3 ) ^{2}}

= - \frac{24}{( 4 x - 3 ) ^{2}}