# a half-derivate or -integral or -fn.

Discussion in 'Mathematics and Physics' started by ci139, May 9, 2017.

1. ### ci139Active Member

Joined:
Apr 12, 2012
Messages:
469
Likes:
37
as for "-- find f (x) so that f (f (x)) = exp (x) --"
,
find a halfDerivate[exp(x)] = exp^( '/2) [x] -- as for a^x = a^(x/2)·a^(x/2) the exp ' (x) = exp^( '/2) [x] "unknown operator" exp^( '/2) [x]

it's something like find half limit for Lim_(x→0) Sin(x) = halfLim_(x→0) Sin(x) "unknown operator" halfLim_(x→0) Sin(x)

(the target here is a "fraction space" in between "function space" and it's "differential space" so that the value 0.5 (a half) might be any fraction)

the speciffic target here is "fraction space" for fraction 0.5 and the function exp(x)

2. ### RatchitWell-Known Member

Joined:
Mar 12, 2008
Messages:
1,948
Likes:
83
Is there a question within your incoherent posting?

Ratch

3. ### ci139Active Member

Joined:
Apr 12, 2012
Messages:
469
Likes:
37
What difference would that make?
Surprisingly your question contains a partial answer - as the wandering from function to it's derivate may turn out to be non-homogenous non-linear e.g. an incoherent travel - that also might not describe due limited scope and -vocabulary of today's math.

Last edited: May 9, 2017