# growth rate of functions

Let $m$ and $n$ be positive integers, c a positive real number. The following functions all tend to $\infty$ as $x \to \infty$ and they are arranged in order of increasing growth rate:
$\ln(x), \! x^{1/m}, \! x^n, \! e^{cx}, \! e^{x^{n}}$
(a) Where in the list would you place $x^x$ and $\frac{x}{\ln(x)}?$