derivative of \sqrt[3]{x}-(10/x)

解

\frac{d}{d x} (3 x - \frac{10}{x})

\frac{x ^{2} + 30 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

解答ステップ

\frac{d}{d x} (3 x - \frac{10}{x})

和/差の法則を適用:

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

= \frac{d}{d x} (3 x) - \frac{d}{d x} (\frac{10}{x})

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

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

= \frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{10}{x ^{2}})

簡素化

\frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{10}{x ^{2}}) : \frac{x ^{2} + 30 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

= \frac{x ^{2} + 30 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}