derivative of ln^3(2x+5)

解

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

\frac{6 ln ^{2} ( 2 x + 5 )}{2 x + 5}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (ln (2 x + 5)) = \frac{2}{2 x + 5}

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

簡素化

3 ln^{2} (2 x + 5) \frac{2}{2 x + 5} : \frac{6 ln ^{2} ( 2 x + 5 )}{2 x + 5}

= \frac{6 ln ^{2} ( 2 x + 5 )}{2 x + 5}