derivative (1+(10)/x)^8

解

導関数

(1 + \frac{10}{x})^{8}

- \frac{80 ( x + 10 ) ^{7}}{x ^{9}}

解答ステップ

\frac{d}{d x} ((1 + \frac{10}{x})^{8})

連鎖法則を適用:

8 (1 + \frac{10}{x})^{7} \frac{d}{d x} (1 + \frac{10}{x})

= 8 (1 + \frac{10}{x})^{7} \frac{d}{d x} (1 + \frac{10}{x})

\frac{d}{d x} (1 + \frac{10}{x}) = - \frac{10}{x ^{2}}

= 8 (1 + \frac{10}{x})^{7} (- \frac{10}{x ^{2}})

簡素化

8 (1 + \frac{10}{x})^{7} (- \frac{10}{x ^{2}}) : - \frac{80 ( x + 10 ) ^{7}}{x ^{9}}

= - \frac{80 ( x + 10 ) ^{7}}{x ^{9}}