derivative of 8cos^2(x)

解

\frac{d}{d x} (8 cos^{2} (x))

- 8 sin (2 x)

解答ステップ

\frac{d}{d x} (8 cos^{2} (x))

定数を除去:

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

= 8 \frac{d}{d x} (cos^{2} (x))

連鎖法則を適用:

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

= 2 cos (x) \frac{d}{d x} (cos (x))

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

= 8 \cdot 2 cos (x) (- sin (x))

簡素化

8 \cdot 2 cos (x) (- sin (x)) : - 8 sin (2 x)

= - 8 sin (2 x)