How to find $f(x)$ in order to find $f^{(10)}(3)$? 
(a) Find the radius of convergence of $\sum_{n=1}^\infty (-1)^n \frac{(x-3)^n}{(2n+1)}$ and its derivative.
(b) Denote by $f(x)$ the function represented by the above power series within its region of convergence. Find $f^{(10)}(3)$, i.e., its 10th derivative at $x = 3$.

I can solve problem (a). However I cannot find f(x). In order to find f(x) how should I do?

Hint:
$$\frac{\arctan \sqrt{x}}{\sqrt{x}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}x^{n}\quad {\text{ for }}|x|\leq 1,x\not =\pm i\!$$
$$x\rightarrow (x-3)$$
$$\frac{\arctan \sqrt{x-3}}{\sqrt{x-3}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}(x-3)^{n}\quad {\text{ for }}|x-3|\leq 1$$
