# Limit question mixed with derivatives…?

Find $$\lim_{x\to a} \frac{f(x)-f(a)}{(x-a)}$$ if $f(x)$ is derivable in the point $a$.

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Please, try to make the title of your question more informative. E.g., Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. –  Julian Kuelshammer Nov 11 '12 at 13:47
What is your definition of "$f(x)$ is derivable in the point $a$"? –  Dennis Gulko Nov 11 '12 at 13:56
The answer to your question it is $f^{\prime}(a)$.
And, this is just by definition. If it happened that $f'(a)$ was defined using an $h\to 0$ in the denominator, instead of $(x-a)$, then you also need the substitution $h:=x-a$. –  Berci Nov 11 '12 at 14:05
@Amr: I used the formatting $f^\prime (a)$. You can pick up a lot of formatting knowledge by hovering over a formatted expression and "right-clicking" - then click "show math as" then click on "TeX" and a pop-up window will appear with the formatted expression (which then needs to be enclosed in dollar signs for this site). –  amWhy Nov 11 '12 at 14:57