**1. The problem statement, all variables and given/known data**
Hi there. I got next problem, and I must say if it is differentiable in all of its domain.

So, I thought trying with the partial derivatives.

And here is the deal. As you see, I've calculated by definition that for all points of the form

the derivative is zero. But the limit of the derivative tending to that kind of points doesn't exists because of the cosine. Is there something wrong with this? I mean is there any kind of contradiction with this, or its alright and just the derivative isn't continuous at that kind of points?

Bye and thanks.