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

Explanation

1. 01

   Three layers: the square, then the sine, then $3x$. Differentiate each and multiply.

2. 02

   $2\sin 3x \cdot \cos 3x \cdot 3 = 6\sin 3x\cos 3x = 3\sin 6x$.