How to estimate the $n$-th derivative of a function?

Question

How can I compute the $n$-th derivative of a $C^n$ function evaluated at some point $x_0$? In other words, how can I calculate $f^{(n)}(x_0)$?

I tried by using $$f(x_0)\approx\sum_{k=0}^{n}\binom {n}{k}\frac{(-1)^kf\left(x_0+(n−2k)h\right)}{(2h)^n}$$ but I did not get good results. Thank you!