derivative of (1+7/x ^5)

解

\frac{d}{d x} ((1 + \frac{7}{x})^{5})

- \frac{35 ( x + 7 ) ^{4}}{x ^{6}}

解答ステップ

\frac{d}{d x} ((1 + \frac{7}{x})^{5})

連鎖法則を適用:

5 (1 + \frac{7}{x})^{4} \frac{d}{d x} (1 + \frac{7}{x})

= 5 (1 + \frac{7}{x})^{4} \frac{d}{d x} (1 + \frac{7}{x})

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

= 5 (1 + \frac{7}{x})^{4} (- \frac{7}{x ^{2}})

簡素化

5 (1 + \frac{7}{x})^{4} (- \frac{7}{x ^{2}}) : - \frac{35 ( x + 7 ) ^{4}}{x ^{6}}

= - \frac{35 ( x + 7 ) ^{4}}{x ^{6}}