# Math Help - Power series

1. ## Power series

Find $f^9(0)$.

$f(x)=xcosx^2$

I'm not sure where to start, then again I don't understand most of the calculus I do...

but so far I have $x(1-\frac{(x^2)^2}{2!}+\frac{(x^2)^4}{4!}-\frac{(x^2)^6}{6!}+...)$

then

$(x-\frac{x^5}{2!}+\frac{x^9}{4!}-\frac{x^13}{6!}+...)$

and I'm guessing I need to write it as a sum. (on the interval of convergence a power series is the taylor series of its sum). But I'm not sure what the question is asking exactly.

2. does $\frac{9!}{4!}=15120$ sound right?