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

解

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

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

解答ステップ

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

商の法則を適用:

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

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

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

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

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

簡素化

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

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