# Tetration Forum

Full Version: Algoritmization of parametric derivation
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I have a really strange f function (that I would like to take into Carleman matrices) so I need the derivative of its powers. We have just know about the function that:
$\int f dx = F$
${dF \over dx} = f$
${df \over dx} = a/F$ where a is a constant.
I am interested in the following expression:
${d^N \over dx^N} f^M = ?$
A recursive formula is not the best, but really enough. Not to be in PARI/gp is not the best, but enough.
(It is important for me to invastigate the infinite Taylor series with argument infinity.)