derivative of ((x+3/(x-3))^4)

解

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

- \frac{24 ( x + 3 ) ^{3}}{( x - 3 ) ^{5}}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (\frac{x + 3}{x - 3}) = - \frac{6}{( x - 3 ) ^{2}}

= 4 (\frac{x + 3}{x - 3})^{3} (- \frac{6}{( x - 3 ) ^{2}})

簡素化

4 (\frac{x + 3}{x - 3})^{3} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{24 ( x + 3 ) ^{3}}{( x - 3 ) ^{5}}

= - \frac{24 ( x + 3 ) ^{3}}{( x - 3 ) ^{5}}