derivative ln(X^{1/2})

解

導関数

ln (X^{\frac{1}{2}})

\frac{1}{2 X}

解答ステップ

\frac{d}{d X} (ln (X^{\frac{1}{2}}))

連鎖法則を適用:

\frac{1}{X ^{\frac{1}{2}}} \frac{d}{d X} (X^{\frac{1}{2}})

= \frac{1}{X ^{\frac{1}{2}}} \frac{d}{d X} (X^{\frac{1}{2}})

\frac{d}{d X} (X^{\frac{1}{2}}) = \frac{1}{2 X ^{\frac{1}{2}}}

= \frac{1}{X ^{\frac{1}{2}}} \cdot \frac{1}{2 X ^{\frac{1}{2}}}

簡素化

\frac{1}{X ^{\frac{1}{2}}} \cdot \frac{1}{2 X ^{\frac{1}{2}}} : \frac{1}{2 X}

= \frac{1}{2 X}