For a rational/irrational function, determine where f is differentiable

This relates to a previous question I asked, so we can somewhat pick up from there.

For the function

determine at which points is differentiable.

I already know that is continuous ONLY at the point , so that's the only potential location for where could be differentiable. Showing whether or not it is, however, is the trick.

Would using this trick work?

when

I only need to determine whether or not as to prove whether or not the function is differentiable at .