The "little" differential operator and applications to tetration

[JmsNxn]

you asked for a function f such that little derivative = little geo derivative ?

i was talking about that.

oh no no, I was asking for a function f that satisfied this identity:

\( 1:\frac{d*}{dx}f(x) = e^{1:\frac{d}{dx} f(x-1)} \)

where the left side is the little geometric derivative and the right side is e to the power of the little derivative of f(x-1).

I just have a curiosity that this function is related to tetration; because tetration satisfies:
\( \frac{d*}{dx}sexp(x) = e^{\frac{d}{dx}sexp(x-1)} \)

but it's just a hunch.