Functions of the form c^x are called exponential when c is a constant. How about the function x^x? It seems somewhere in between exponential and double exponential to me. Is there a good way to describe it?

Arendrogfkl

Arendrogfkl

Answered question

2022-11-16

Functions of the form c x are called exponential when c is a constant.
How about the function x x ? It seems somewhere in between exponential and double exponential to me. Is there a good way to describe it?

Answer & Explanation

motylowceyvy

motylowceyvy

Beginner2022-11-17Added 19 answers

Regarding "describing the function": note that
x x = e x ln x
So indeed, we may state that (asymptotically) e x x x e x 2 .
inurbandojoa

inurbandojoa

Beginner2022-11-18Added 11 answers

It is not an exponential function. A function is called exponential if f ( x ) = a x where a>0 , a 1, and a is constant.

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