The question is find dy/dx of $\displaystyle \frac{1}{4}\sin^2(2x)$.

which I rewrote as $\displaystyle \frac{1}{4}(\sin2x)^2$

then, using the chain rule, $\displaystyle \frac{1}{2}\sin2x\cos2x$.

But the book gives the answer $\displaystyle \frac{1}{2}\sin4x$.

Is my answer wrong? Or do I just need to simplify it further?