derivative f(x)=((x+2)/(x-2))^5

解

導関数

f (x) = (\frac{x + 2}{x - 2})^{5}

- \frac{20 ( x + 2 ) ^{4}}{( x - 2 ) ^{6}}

解答ステップ

\frac{d}{d x} ((\frac{x + 2}{x - 2})^{5})

連鎖法則を適用:

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

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

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

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

簡素化

5 (\frac{x + 2}{x - 2})^{4} (- \frac{4}{( x - 2 ) ^{2}}) : - \frac{20 ( x + 2 ) ^{4}}{( x - 2 ) ^{6}}

= - \frac{20 ( x + 2 ) ^{4}}{( x - 2 ) ^{6}}