There are several different ways to do this, depending on what you can or want to use.
Of course, a function of one variable is "differentiable" at x= a if and only if exists. It is NOT differentiable if that limit does not exist. So you could show that does not exist.
Or you could use the fact that, while the derivative of a function is not necessarily continuous, it does have the "intermediate value property". In particular, if the derivative at x= a exists, then . So what is the derivative of ? What is the limit of that derivative as x goes to 0?