derivative \sqrt[5]{x^4}-5/x

解

導関数

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

\frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}} + \frac{5}{x ^{2}}

解答ステップ

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

和/差の法則を適用:

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

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

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

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

= \frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}} - (- \frac{5}{x ^{2}})

簡素化

= \frac{4 x ^{3}}{5 ( x ^{4} ) ^{\frac{4}{5}}} + \frac{5}{x ^{2}}