derivative 3ln(6x+1)

解

導関数

3 ln (6 x + 1)

\frac{18}{6 x + 1}

解答ステップ

\frac{d}{d x} (3 ln (6 x + 1))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (ln (6 x + 1))

連鎖法則を適用:

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

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

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

= 3 \cdot \frac{1}{6 x + 1} \cdot 6

簡素化

3 \cdot \frac{1}{6 x + 1} \cdot 6 : \frac{18}{6 x + 1}

= \frac{18}{6 x + 1}