derivative of 5cos^2(x)

解答

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

- 5 sin (2 x)

求解步骤

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

将常数提出:

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

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

使用连锁律:

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)

= 5 \cdot 2 cos (x) (- sin (x))

化简

5 \cdot 2 cos (x) (- sin (x)) : - 5 sin (2 x)

= - 5 sin (2 x)