Define differentiability of a function at a point.

Let $f(x)$ be a real valued function defined on an open interval $(a, b)$ and let $c \in(a, b)$.

Then $f(x)$ is said to be differentiable or derivable at $x=c$ iff

$\lim _{x \rightarrow c} \frac{f(x)-f(c)}{x-c}$ exists finitely.

or, $f^{\prime}(c)=\lim _{x \rightarrow c} \frac{f(x)-f(c)}{x-c}$