# Derivatives question, I need this now? [closed]

I have to find the $$\lim_{x\to a} \frac{f(x)-f(a)}{x-a}$$ I know that the result is $f'(a)$, but how do I get until there?

-
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. –  amWhy Nov 11 '12 at 20:41
possible duplicate of Limit question mixed with derivatives...? –  Cameron Buie Nov 11 '12 at 23:54

## closed as not a real question by Will Hunting, TMM, rschwieb, Norbert, Cameron BuieNov 11 '12 at 23:54

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

I'm going to assume that your definition of the derivative at $a$ is

$$\lim_{h\rightarrow 0} \frac{f(a+h) - f(a)}{h}.$$

So substituting $x = a + h$ we get

$$f'(a) = \lim_{h\rightarrow 0} \frac{f(a+h) - f(a)}{h} = \lim_{x - a \rightarrow 0}\frac{f(x) - f(a)}{a + h - a} = \lim_{x \rightarrow a} \frac{f(x) - f(a)}{x-a}$$

-

This is the definition of the derivative.

-
I presume your definition of derivative is $$f^{'}(a)=\lim_{h\to 0} \frac{f(a+h)-f(a)}{h}.$$
$$\lim_ {x\to a} \frac{f(x)-f(a)}{x-a}=f'(a)$$ is definition of derivative of function $f$ at $x=a$