derivative of 4x^{-1/3}+9/(x^{5/3})

解

\frac{d}{d x} (4 x^{- \frac{1}{3}} + \frac{9}{x ^{\frac{5}{3}}})

- \frac{4}{3 x ^{\frac{4}{3}}} - \frac{15}{x ^{\frac{8}{3}}}

解答ステップ

\frac{d}{d x} (4 x^{- \frac{1}{3}} + \frac{9}{x ^{\frac{5}{3}}})

和/差の法則を適用:

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

= \frac{d}{d x} (4 x^{- \frac{1}{3}}) + \frac{d}{d x} (\frac{9}{x ^{\frac{5}{3}}})

\frac{d}{d x} (4 x^{- \frac{1}{3}}) = - \frac{4}{3 x ^{\frac{4}{3}}}

\frac{d}{d x} (\frac{9}{x ^{\frac{5}{3}}}) = - \frac{15}{x ^{\frac{8}{3}}}

= - \frac{4}{3 x ^{\frac{4}{3}}} - \frac{15}{x ^{\frac{8}{3}}}