exp(x) x f ' (exp(x)) = exp(f(x)) f(x)

[tommy1729]

A simple idea comes to mind for x > 1 :

semi-exp(x) is locally about equal to

exp^[v]( c ln^[v](x) )

where v is log*(x) 

see 

https://en.wikipedia.org/wiki/Iterated_logarithm

and c is some constant between 1 and 2 , probably sqrt(2).



regards

tommy1729