derivative 4cos(5ln(x))

解

導関数

4 cos (5 ln (x))

- \frac{20 sin ( 5 ln ( x ) )}{x}

解答ステップ

\frac{d}{d x} (4 cos (5 ln (x)))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (cos (5 ln (x)))

連鎖法則を適用:

- sin (5 ln (x)) \frac{d}{d x} (5 ln (x))

= - sin (5 ln (x)) \frac{d}{d x} (5 ln (x))

\frac{d}{d x} (5 ln (x)) = \frac{5}{x}

= 4 (- sin (5 ln (x)) \frac{5}{x})

簡素化

4 (- sin (5 ln (x)) \frac{5}{x}) : - \frac{20 sin ( 5 ln ( x ) )}{x}

= - \frac{20 sin ( 5 ln ( x ) )}{x}