The constant term is 0 as usual. The first non-zero term is (include power of x as well as its coefficient):

according to the book

f(x)=f(0)+f'(0)x+f''(0)x^2/2!+f'''(0)x^3/3!...

so I think the first non zero term is

f'(0) = cos(x^2)2x

but substituting x with 0, the term will be zero

and there will always be an x in the expression if I keep differentiating.

So how do I do it?

THANKS!