derivative of (x-1/(x^2)^5)

解

\frac{d}{d x} ((x - \frac{1}{x ^{2}})^{5})

5 (x - \frac{1}{x ^{2}})^{4} (1 + \frac{2}{x ^{3}})

解答ステップ

\frac{d}{d x} ((x - \frac{1}{x ^{2}})^{5})

連鎖法則を適用:

5 (x - \frac{1}{x ^{2}})^{4} \frac{d}{d x} (x - \frac{1}{x ^{2}})

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

\frac{d}{d x} (x - \frac{1}{x ^{2}}) = 1 + \frac{2}{x ^{3}}

= 5 (x - \frac{1}{x ^{2}})^{4} (1 + \frac{2}{x ^{3}})