derivative of ((x+3/(x-3))^5)

解

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

- \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

解答ステップ

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

連鎖法則を適用:

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

= 5 (\frac{x + 3}{x - 3})^{4} \frac{d}{d x} (\frac{x + 3}{x - 3})

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

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

簡素化

5 (\frac{x + 3}{x - 3})^{4} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

= - \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}