derivative of (ln(2x+1)^{1/2})

解

\frac{d}{d x} ((ln (2 x + 1))^{\frac{1}{2}})

\frac{1}{ln ^{\frac{1}{2}} ( 2 x + 1 ) ( 2 x + 1 )}

解答ステップ

\frac{d}{d x} ((ln (2 x + 1))^{\frac{1}{2}})

連鎖法則を適用:

\frac{1}{2 ln ^{\frac{1}{2}} ( 2 x + 1 )} \frac{d}{d x} (ln (2 x + 1))

= \frac{1}{2 ln ^{\frac{1}{2}} ( 2 x + 1 )} \frac{d}{d x} (ln (2 x + 1))

\frac{d}{d x} (ln (2 x + 1)) = \frac{2}{2 x + 1}

= \frac{1}{2 ln ^{\frac{1}{2}} ( 2 x + 1 )} \cdot \frac{2}{2 x + 1}

簡素化

\frac{1}{2 ln ^{\frac{1}{2}} ( 2 x + 1 )} \cdot \frac{2}{2 x + 1} : \frac{1}{ln ^{\frac{1}{2}} ( 2 x + 1 ) ( 2 x + 1 )}

= \frac{1}{ln ^{\frac{1}{2}} ( 2 x + 1 ) ( 2 x + 1 )}