# Definition of the Derivative using delta and epsilon

## Main Question or Discussion Point

Hi,

I have a question about the formulation of the derivative. The definition is

$$f'(x_0)=\lim_{x\rightarrow x_0}\frac{f(x)-f(x_0)}{x-x_0}[/itex] Lets say this limit exists. Can I write the limit in the typical $\epsilon-\delta$ method as such Given the limit exists, then for all $\epsilon>0$ there exists a $\delta>0$ such that $|x-x_0|<\delta\implies$ [tex]\left|\frac{f(x)-f(x_0)}{x-x_0}-f'(x_0)\right|<\epsilon$$

?