calculus - Differntiable and continuous

Is it true that a function which is not continuous at a point will not be differentiable at that point? Graphically it seems so, but can we prove this formally?
Also, if the above statement is incorrect, can we still disprove it?

Note that we know "All differentiable functions are continuous, but not all continuous functions are differentiable". But I am asking about the negation of this in some sense