y=sin(x^2)cos(x^2) find the derivative

I think I'm supposed to do the product rule and I get sin(x^2)-sin(x^2)+cos(x^2)cos(x^)2

But what do I do after that?

Question

y=sin(x^2)cos(x^2) find the derivative

I think I'm supposed to do the product rule and I get sin(x^2)-sin(x^2)+cos(x^2)cos(x^)2

But what do I do after that?

anonymous · Answer

missing the chair rule

anonymous · Answer

*chain rule

anonymous · Answer

easiest to keep from getting bogged down in trig is to recall that 
$$\sin(x)\cos(x)=\frac{1}{2}\sin(2x)$$

anonymous · Answer

so you have 
$$\frac{1}{2}\sin(2x^2)$$ take the derivative using the chain rule get 
$$\frac{1}{2}\cos(2x^2)\times 4x$$
$$2x\cos(2x^2)$$

anonymous · Answer

otherwise using chain and product rule it is a big fat mess

anonymous · Answer

That makes it so much easier. Ya the chain rule was getting pretty busy. Thanks.