derivative ln((1+3x)^2)

解

導関数

ln ((1 + 3 x)^{2})

\frac{6}{1 + 3 x}

解答ステップ

\frac{d}{d x} (ln ((1 + 3 x)^{2}))

連鎖法則を適用:

\frac{1}{( 1 + 3 x ) ^{2}} \frac{d}{d x} ((1 + 3 x)^{2})

= \frac{1}{( 1 + 3 x ) ^{2}} \frac{d}{d x} ((1 + 3 x)^{2})

\frac{d}{d x} ((1 + 3 x)^{2}) = 6 (1 + 3 x)

= \frac{1}{( 1 + 3 x ) ^{2}} \cdot 6 (1 + 3 x)

簡素化

\frac{1}{( 1 + 3 x ) ^{2}} \cdot 6 (1 + 3 x) : \frac{6}{1 + 3 x}

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