derivative of tan^2(xcos(x))

解

\frac{d}{d x} (tan^{2} (x) cos (x))

sin (x) (1 + sec^{2} (x))

解答ステップ

\frac{d}{d x} (tan^{2} (x) cos (x))

簡素化

tan^{2} (x) cos (x) : sin (x) tan (x)

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

積の法則を適用:

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

f = sin (x), g = tan (x)

= \frac{d}{d x} (sin (x)) tan (x) + \frac{d}{d x} (tan (x)) sin (x)

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= cos (x) tan (x) + sec^{2} (x) sin (x)

簡素化

cos (x) tan (x) + sec^{2} (x) sin (x) : sin (x) (1 + sec^{2} (x))

= sin (x) (1 + sec^{2} (x))