derivative f(x)=(1+cos^2(x))^6

解

導関数

f (x) = (1 + cos^{2} (x))^{6}

- 6 sin (2 x) (1 + cos^{2} (x))^{5}

解答ステップ

\frac{d}{d x} ((1 + cos^{2} (x))^{6})

連鎖法則を適用:

6 (1 + cos^{2} (x))^{5} \frac{d}{d x} (1 + cos^{2} (x))

= 6 (1 + cos^{2} (x))^{5} \frac{d}{d x} (1 + cos^{2} (x))

\frac{d}{d x} (1 + cos^{2} (x)) = - sin (2 x)

= 6 (1 + cos^{2} (x))^{5} (- sin (2 x))

簡素化

= - 6 sin (2 x) (1 + cos^{2} (x))^{5}