derivative of (1+cos(2x)^2)

解

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

- 16 cos^{3} (x) sin (x)

解答ステップ

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

簡素化

(1 + cos (2 x))^{2} : 4 cos^{4} (x)

= \frac{d}{d x} (4 cos^{4} (x))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (cos^{4} (x))

連鎖法則を適用:

4 (cos (x))^{3} \frac{d}{d x} (cos (x))

= 4 (cos (x))^{3} \frac{d}{d x} (cos (x))

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

= 4 \cdot 4 (cos (x))^{3} (- sin (x))

簡素化

= - 16 cos^{3} (x) sin (x)