derivative y=xln(sin^2(x))

解

導関数

y = x ln (sin^{2} (x))

ln (sin^{2} (x)) + 2 x cot (x)

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (sin^{2} (x))

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

\frac{d x}{d x} = 1

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

= 1 \cdot ln (sin^{2} (x)) + 2 cot (x) x

簡素化

= ln (sin^{2} (x)) + 2 x cot (x)