I'm doing some Calculus homework on linear approximations and differentials right now, and I'm stuck trying to find the differential of this function:

f(x)= x^2 sin2x

My book says that the answer is dy= 2x(xcos2x + sin2x)dx, but I cannot reproduce that answer. I think that this derivative may have something to do with the double angle formulas for sin2x and cos2x, but I don't know where to begin. Will someone please show my how to find this derivative?

Thanks,

Zach