Q:

Why is $e$ a good base to use whenever you have a moving exponent

While trying to evaluate a limit involving $x^x$ our professor told us that whenever dealing with moving exponents the best thing to do is to use "base $e$", why is that?

A:

Using $e$ simplifies lot of calculation, because number $e$ itself is the result of simple analytic processes. We can use any other number like $2$ and write $x^x=2^{x\log_{2}x}$ but then the derivatives of $2^x$ and $\log_{2}x$ don't have as simple forms as those of $e^x, \log x$. The functions $e^x, \log x$ have been created to have simple derivatives.

