From the existence of the limit of derivatives we can conclude the differentiability.

Question

it should actually be quite easy but i have difficulties to prove this fact: if $f: \mathbb{R} \to \mathbb{R}$ is continuous everewhere and is differentiable everywhere except for $x_0$ and if $\lim_{x\to x_0}f^{'}(x)$ exists, then $f^{'}(x_0)$ exists. Could someone help please? Thanks.