derivative of ln(x^{1/5})

解

\frac{d}{d x} (ln (x^{\frac{1}{5}}))

\frac{1}{5 x}

解答ステップ

\frac{d}{d x} (ln (x^{\frac{1}{5}}))

連鎖法則を適用:

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

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

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

= \frac{1}{x ^{\frac{1}{5}}} \cdot \frac{1}{5 x ^{\frac{4}{5}}}

簡素化

\frac{1}{x ^{\frac{1}{5}}} \cdot \frac{1}{5 x ^{\frac{4}{5}}} : \frac{1}{5 x}

= \frac{1}{5 x}