derivative of ((x+1/(x-1))^4)

解

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

- \frac{8 ( x + 1 ) ^{3}}{( x - 1 ) ^{5}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

4 (\frac{x + 1}{x - 1})^{3} (- \frac{2}{( x - 1 ) ^{2}}) : - \frac{8 ( x + 1 ) ^{3}}{( x - 1 ) ^{5}}

= - \frac{8 ( x + 1 ) ^{3}}{( x - 1 ) ^{5}}