There are severaldifferentways to do this, depending on what you can or want to use.

Of course, a function of one variableis"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, itdoeshave the "intermediate value property". In particular, if the derivative at x= a exists, then . So whatisthe derivative of ? What is the limit of that derivative as x goes to 0?