derivative ln(\sqrt[6]{x})

解

導関数

ln (6 x)

\frac{1}{6 6 x x ^{\frac{5}{6}}}

解答ステップ

\frac{d}{d x} (ln (6 x))

連鎖法則を適用:

\frac{1}{6 x} \frac{d}{d x} (6 x)

= \frac{1}{6 x} \frac{d}{d x} (6 x)

\frac{d}{d x} (6 x) = \frac{1}{6 x ^{\frac{5}{6}}}

= \frac{1}{6 x} \cdot \frac{1}{6 x ^{\frac{5}{6}}}

簡素化

\frac{1}{6 x} \cdot \frac{1}{6 x ^{\frac{5}{6}}} : \frac{1}{6 6 x x ^{\frac{5}{6}}}

= \frac{1}{6 6 x x ^{\frac{5}{6}}}