derivative of ln((x+6^{11}))

解

\frac{d}{d x} (ln ((x + 6)^{11}))

\frac{11}{x + 6}

解答ステップ

\frac{d}{d x} (ln ((x + 6)^{11}))

連鎖法則を適用:

\frac{1}{( x + 6 ) ^{11}} \frac{d}{d x} ((x + 6)^{11})

= \frac{1}{( x + 6 ) ^{11}} \frac{d}{d x} ((x + 6)^{11})

\frac{d}{d x} ((x + 6)^{11}) = 11 (x + 6)^{10}

= \frac{1}{( x + 6 ) ^{11}} \cdot 11 (x + 6)^{10}

簡素化

\frac{1}{( x + 6 ) ^{11}} \cdot 11 (x + 6)^{10} : \frac{11}{x + 6}

= \frac{11}{x + 6}