derivative of ((1-2x/(1+x))^3)

解

\frac{d}{d x} ((\frac{1 - 2 x}{1 + x})^{3})

- \frac{9 ( 1 - 2 x ) ^{2}}{( 1 + x ) ^{4}}

解答ステップ

\frac{d}{d x} ((\frac{1 - 2 x}{1 + x})^{3})

連鎖法則を適用:

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

= 3 (\frac{1 - 2 x}{1 + x})^{2} \frac{d}{d x} (\frac{1 - 2 x}{1 + x})

\frac{d}{d x} (\frac{1 - 2 x}{1 + x}) = - \frac{3}{( 1 + x ) ^{2}}

= 3 (\frac{1 - 2 x}{1 + x})^{2} (- \frac{3}{( 1 + x ) ^{2}})

簡素化

3 (\frac{1 - 2 x}{1 + x})^{2} (- \frac{3}{( 1 + x ) ^{2}}) : - \frac{9 ( 1 - 2 x ) ^{2}}{( 1 + x ) ^{4}}

= - \frac{9 ( 1 - 2 x ) ^{2}}{( 1 + x ) ^{4}}