Infinite tetration and superroot of infinitesimal

[Ivars]

Sure, but what is dx^(1/dx) or f(x)^(1/f(x)) from Your example?

I know from Euler that ln((1+dx)^(1/dx))= 1 so (1+dx)^(1/dx) = e.

But what about dx^(1/dx)?

Ivars