Guys I am sorry if this question has been asked before, but it has been pestering me for long time. It is about the notation of derivatives using 'prime'.

If f(x) is a function of x, then does f'(a) represent f(a) differentiated with respect to a, or does it represent f(x) differentiated with respect to x where x=a or are they both the same thing?

Forgive the lack of Latex sophistication.