I'm trying to differentiate $\displaystyle \sin^2(2x)$ but it's not going very well.

The answer is 2sin(4x).

To me it seems natural to use the chain rule and get 2sin(2x) and then multiplied with the derivative of sin(2x) which is 2cos(2x). So my gut tells me the answer is 2sin(2x)*2cos(2x) but that's obviously wrong.

Any insight is well appreciated. Thanks.