derivative f(x)=ln(9sin^2(x))

解

導関数

f (x) = ln (9 sin^{2} (x))

2 cot (x)

解答ステップ

\frac{d}{d x} (ln (9 sin^{2} (x)))

連鎖法則を適用:

\frac{1}{9 sin ^{2} ( x )} \frac{d}{d x} (9 sin^{2} (x))

= \frac{1}{9 sin ^{2} ( x )} \frac{d}{d x} (9 sin^{2} (x))

\frac{d}{d x} (9 sin^{2} (x)) = 9 sin (2 x)

= \frac{1}{9 sin ^{2} ( x )} \cdot 9 sin (2 x)

簡素化

\frac{1}{9 sin ^{2} ( x )} \cdot 9 sin (2 x) : 2 cot (x)

= 2 cot (x)