Functions that are always less than their derivatives I was wondering if there are functions for which $$f'(x) > f(x)$$ for all $x$. Only examples I could think of were $e^x - c$ and simply $- c$ in which $c > 0$. Also, is there any significance in a function that is always less than its derivative?

Edit: Thank you very much for all the replies. It seems almost all functions that apply are exponential by nature... 
Are there more examples like - 1/x?
Again are there any applications/physical manifestations of these functions? [for example an object with a velocity that is always greater than its position/acceleration  is always greater than its velocity]

The inequality $$f'(x) > f(x)$$ is equivalent to $$\left[ f(x) e^{-x} \right]' > 0.$$
So the general solution is to take any differentiable function $g(x)$ with $g'(x) > 0$ and put $f(x) = g(x) e^x$. 
Note that nothing is assumed about $f$ except differentiability, which is necessary to ask the question in the first place. 
