derivative f(x)=x^{5/3}-x^{2/3}

解

導関数

f (x) = x^{\frac{5}{3}} - x^{\frac{2}{3}}

\frac{5 x - 2}{3 x ^{\frac{1}{3}}}

解答ステップ

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

和/差の法則を適用:

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

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

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

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

= \frac{5 x ^{\frac{2}{3}}}{3} - \frac{2}{3 x ^{\frac{1}{3}}}

簡素化

\frac{5 x ^{\frac{2}{3}}}{3} - \frac{2}{3 x ^{\frac{1}{3}}} : \frac{5 x - 2}{3 x ^{\frac{1}{3}}}

= \frac{5 x - 2}{3 x ^{\frac{1}{3}}}