Math Help - Derivative

1. Derivative

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

2. Product rule yields:

2x sin2x + 2x² cos2x.

Now factoring:

2x(sin 2x + x cos 2x)

Then it's done.

3. Re:

Hi Zachb hope all is going well. I worked the problem out, then gave you for future reference an easy way to solve these types of derivatives. Just click on the link below.

Best of luck!