derivative of cos(3ln(x))

解

\frac{d}{d x} (cos (3 ln (x)))

- \frac{3 sin ( 3 ln ( x ) )}{x}

解答ステップ

\frac{d}{d x} (cos (3 ln (x)))

連鎖法則を適用:

- sin (3 ln (x)) \frac{d}{d x} (3 ln (x))

= - sin (3 ln (x)) \frac{d}{d x} (3 ln (x))

\frac{d}{d x} (3 ln (x)) = \frac{3}{x}

= - sin (3 ln (x)) \frac{3}{x}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 sin ( 3 ln ( x ) )}{x}