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

解

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

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

解答ステップ

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

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

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

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

簡素化

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

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