What is $\frac{d}{dx}\left(\cos^{3} 2x\right)$?

Explanation

1. 01

   Three layers: $u^{3}$, then $\cos v$, then $v = 2x$.

2. 02

   $3\cos^{2} 2x \cdot (-\sin 2x) \cdot 2 = -6\cos^{2} 2x\,\sin 2x$.