Calculus intervals differentiability

Question

Hi I have recently come across rolles theorem and the mean value theorem and I noticed that they always assume the function to be differentiable on the open interval (a,b) . i understand that the theorem states this as this is the better argument and the function need not be differentiable on [a,b] but I did read that a function continuous on [a,b] can be differentiable on [a,b] if the derivative at a and the derivative at b are one sided derivatives.the concept of one sided derivatives confuses me a lot I have seen several other questions like this online but none with straightforward explanations.my question is when we say that a function is differentiable on [a,b] do we assume that the derivatives at the end points are one sided?.