On the first derivative of the n-th tetration of f(x)

[tommy1729]

Thank you Daniel! I'll check it out. 
I really hope that a closed formula for the m-th derivative of the n-th tetration of some functions exists. For example for \( f(x)=x \).
So..if \( g(x)={^{n}x} \)
Maybe we can find a closed formula for:
\( \frac{d^{m}}{dx^{m}} {^{n}x} \)
where \( n,m\in\mathbb{N} \) and \( n\geq 2 \)
I have already found somethig interesting, I'll post some of the results I got. Thank you, regards.

That would be interesting , in combinations with ideas like continuum sum etc.

regards

tommy1729