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In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
At x=0 the function is not defined so it makes no sense to ask if they are differentiable there. To be differentiable at a certain point, the function must first of all be defined there! As we head towards x = 0 the function moves up and down faster and faster, so we cannot find a value it is heading towards.