The limit of this function at x=0 is equal to the function value of this function at 0 = 1, which is completely continuous.

But this function is nondifferentiable at x=0. For this unary function, differentiability and differentiability are equivalent.

Differentiable must be continuous. Now y = e | x | is continuous, but not differentiable, which is not inconsistent with the statement that differentiability must be continuous.

If it is complete, it must be differentiable, continuous and continuous is not necessarily differentiable.