derivative f(x)=5x^{4/5}-2x^{2/7}

解

導関数

f (x) = 5 x^{\frac{4}{5}} - 2 x^{\frac{2}{7}}

\frac{4}{x ^{\frac{1}{5}}} - \frac{4}{7 x ^{\frac{5}{7}}}

解答ステップ

\frac{d}{d x} (5 x^{\frac{4}{5}} - 2 x^{\frac{2}{7}})

和/差の法則を適用:

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

= \frac{d}{d x} (5 x^{\frac{4}{5}}) - \frac{d}{d x} (2 x^{\frac{2}{7}})

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

\frac{d}{d x} (2 x^{\frac{2}{7}}) = \frac{4}{7 x ^{\frac{5}{7}}}

= \frac{4}{x ^{\frac{1}{5}}} - \frac{4}{7 x ^{\frac{5}{7}}}