TITLE: Is there another representation for $x^x$
QUESTION [8 upvotes]: I started wondering about this the other day. Since the following have their own alternate representations. $$\begin{align*} \displaystyle\large x+x=2x & \
\frac{x}{x}=1 & xx=x^2\end{align*}$$
Can $x^x$ be represented in some other way? Thanks.

REPLY [9 votes]: $$e^{x\log(x)}$$
This is a nice way to represent it if you want to differentiate it, since you can then just apply the standard differentiation rules. 
Something like $$x^{x^x}$$ will be represented as $$e^{e^{x\log(x)}\log(x)}$$