derivative 3x^{1/3}-5x^{4/3}

解

導関数

3 x^{\frac{1}{3}} - 5 x^{\frac{4}{3}}

\frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

解答ステップ

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (5 x^{\frac{4}{3}}) = \frac{20 x ^{\frac{1}{3}}}{3}

= \frac{1}{x ^{\frac{2}{3}}} - \frac{20 x ^{\frac{1}{3}}}{3}

簡素化

\frac{1}{x ^{\frac{2}{3}}} - \frac{20 x ^{\frac{1}{3}}}{3} : \frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

= \frac{3 - 20 x}{3 x ^{\frac{2}{3}}}