derivative sin(x)ln(cos(x))

解

導関数

sin (x) ln (cos (x))

cos (x) ln (cos (x)) - tan (x) sin (x)

解答ステップ

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

積の法則を適用:

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

f = sin (x), g = ln (cos (x))

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

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

\frac{d}{d x} (ln (cos (x))) = - tan (x)

= cos (x) ln (cos (x)) + (- tan (x)) sin (x)

簡素化

= cos (x) ln (cos (x)) - tan (x) sin (x)