I'm working with this function
$$f(x)=\left(x+\sqrt{x^2-a}\right)^{-b}$$
and I would like to know the $nth$ derivative of $f(x)$. To this end, I ask Wolfram alpha about that given me the following result
$$f^{(n}(x)=\left(x+\sqrt{x^2-a}\right)^{-b-n} (1-b-n)_n$$
where $(x)_n$ means the Pochhammer symbol. (See the link: Wolfram alpha result )
It's easy compare $n=1$ (for example) and one can observe that result is wrong.
Is there something wrong with my procedure? Any help appreciated :)