derivative f(x)=-7x^{4/3}+4/(x^3)

解

導関数

f (x) = - 7 x^{\frac{4}{3}} + \frac{4}{x ^{3}}

\frac{- 28 x ^{\frac{13}{3}} - 36}{3 x ^{4}}

解答ステップ

\frac{d}{d x} (- 7 x^{\frac{4}{3}} + \frac{4}{x ^{3}})

和/差の法則を適用:

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

= - \frac{d}{d x} (7 x^{\frac{4}{3}}) + \frac{d}{d x} (\frac{4}{x ^{3}})

\frac{d}{d x} (7 x^{\frac{4}{3}}) = \frac{28 x ^{\frac{1}{3}}}{3}

\frac{d}{d x} (\frac{4}{x ^{3}}) = - \frac{12}{x ^{4}}

= - \frac{28 x ^{\frac{1}{3}}}{3} - \frac{12}{x ^{4}}

簡素化

- \frac{28 x ^{\frac{1}{3}}}{3} - \frac{12}{x ^{4}} : \frac{- 28 x ^{\frac{13}{3}} - 36}{3 x ^{4}}

= \frac{- 28 x ^{\frac{13}{3}} - 36}{3 x ^{4}}