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

解

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

- \frac{8 ( x + 2 )}{( x - 2 ) ^{3}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{8 ( x + 2 )}{( x - 2 ) ^{3}}