derivative of (cos(x)(ln(tan(x))))

解

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

- sin (x) ln (tan (x)) + 2 csc (2 x) cos (x)

解答ステップ

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (ln (tan (x))) = 2 csc (2 x)

= (- sin (x)) ln (tan (x)) + 2 csc (2 x) cos (x)

簡素化

= - sin (x) ln (tan (x)) + 2 csc (2 x) cos (x)