derivative (5x+1)/(5x-1)

解

導関数

\frac{5 x + 1}{5 x - 1}

- \frac{10}{( 5 x - 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{5 x + 1}{5 x - 1})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 5 x + 1 ) ( 5 x - 1 ) - \frac{d}{d x} ( 5 x - 1 ) ( 5 x + 1 )}{( 5 x - 1 ) ^{2}}

\frac{d}{d x} (5 x + 1) = 5

\frac{d}{d x} (5 x - 1) = 5

= \frac{5 ( 5 x - 1 ) - 5 ( 5 x + 1 )}{( 5 x - 1 ) ^{2}}

簡素化

\frac{5 ( 5 x - 1 ) - 5 ( 5 x + 1 )}{( 5 x - 1 ) ^{2}} : - \frac{10}{( 5 x - 1 ) ^{2}}

= - \frac{10}{( 5 x - 1 ) ^{2}}