look the given relation is valid only for positive integers. its not valid on the full set of real numbers. then the function is not even continuous then how can differential exist?
x+x+x+............(x times) = x*x;.
is valid for number like 1,2
and not for
1.5 or 3.2 or something like that
what (3.2)^(3.2) is is 3.2+.3.2 3.2 times???
the function is discontinuos..