derivative of ((1+x/(1-x))^2)

解

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

\frac{4 ( 1 + x )}{( 1 - x ) ^{3}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

2 \cdot \frac{1 + x}{1 - x} \cdot \frac{2}{( 1 - x ) ^{2}} : \frac{4 ( 1 + x )}{( 1 - x ) ^{3}}

= \frac{4 ( 1 + x )}{( 1 - x ) ^{3}}