
Power series
Find $\displaystyle f^9(0)$.
$\displaystyle f(x)=xcosx^2$
I'm not sure where to start, then again I don't understand most of the calculus I do...
but so far I have $\displaystyle x(1\frac{(x^2)^2}{2!}+\frac{(x^2)^4}{4!}\frac{(x^2)^6}{6!}+...)$
then
$\displaystyle (x\frac{x^5}{2!}+\frac{x^9}{4!}\frac{x^13}{6!}+...)$
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.

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