f(x) / f'(x) puzzle

Enter a trial function f(x) that can depend on up to two parameters a and b.[br][br]The goal is to find a function such that the ratio of the function and its derivative is constant for all x.[br][br]If both x and f(x) are quantities rather than numbers [[b][size=85]see "[i]Semantic Aspects of Quantity[/i]" on the [i]mathMINDhabits[/i] website[/size][/b]] explain how and why this constant can be adjusted.

Information: f(x) / f'(x) puzzle