derivative of cos(xln(cos(x)))

解

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

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

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

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