derivative 5/(x^5)+3/(x^2)

解

導関数

\frac{5}{x ^{5}} + \frac{3}{x ^{2}}

- \frac{25}{x ^{6}} - \frac{6}{x ^{3}}

解答ステップ

\frac{d}{d x} (\frac{5}{x ^{5}} + \frac{3}{x ^{2}})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{5}{x ^{5}}) + \frac{d}{d x} (\frac{3}{x ^{2}})

\frac{d}{d x} (\frac{5}{x ^{5}}) = - \frac{25}{x ^{6}}

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

= - \frac{25}{x ^{6}} - \frac{6}{x ^{3}}