derivative of (sin(ln(x))^2)

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (sin (ln (x))) = \frac{cos ( ln ( x ) )}{x}

= 2 sin (ln (x)) \frac{cos ( ln ( x ) )}{x}

簡素化

2 sin (ln (x)) \frac{cos ( ln ( x ) )}{x} : \frac{sin ( 2 ln ( x ) )}{x}

= \frac{sin ( 2 ln ( x ) )}{x}