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?

Answer 1

missing the chair rule

Answer 2

*chain rule

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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