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I have a very complicated function

$f(x,y)= \Gamma{(a+ \sqrt{a-x^2})} \Gamma{(a- \sqrt{a-x^2})} \ _2F_1(b+\sqrt{a-x^2},b-\sqrt{a-x^2},2,1+y/4)$

$a>0$

I would like to know the expresion of the nth $x$ derivative of $f$ but as that is too complicated, is there any way to at least have an aproximate form or bounds of the nth derivatives?

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