Let $f(x)=x^x$. The derivative $f'(x)$ can be written as the product $f(x)g(x)$ for a certain function $g(x)$. Find $g(x)$.
By the chain rule, g(x) = log(x) + x.
Sorry, that's not correct. Maybe it's possible to rewrite $x^x$ in terms of an exponential with base $e$?