Functions in a bar

The Joke

All the function are gathered in a bar, drinking, chatting and relaxing. Suddenly, the $x^2$ function enters the bar shouting with scare

- Run, run quickly, derivatives are coming and they are angry.

Then the exponential function, $e^x$ stands up, makes a step and says proudly

- Let them come, I am not afraid!

Background
When a derivative acts on function it usually changes the function's form. For example the derivative of the polynomial function decreases its order, e.g. $d/dx (x^n) = n x^{n-1}$, where $n$ is integer, but the result is valid for non-polynomial functions ($n$ real) too. Other common derivatives regard the $sin x$ and $cos x$ functions, where $d/dx (sin x) = cos x$ and $d/dx (cos x) = - sin x $.

The only exception is the exponential function $e^x$ whose derivatives always give the exponential function again, i.e. $d/dx (e^x) = e^x$.