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**Ulysses** **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.

$\displaystyle f(x,y)=\begin{Bmatrix} (x+y)^2\sen(\displaystyle\frac{\pi}{x+y}) & \mbox{ si }& y\neq{-x}\\0 & \mbox{si}& y=-x\end{matrix}$

So, I thought trying with the partial derivatives.

$\displaystyle f_x=\begin{Bmatrix} 2(x+y)\sen(\displaystyle\frac{\pi}{x+y})-\pi\cos(\displaystyle\frac{\pi}{x+y}) & \mbox{ si }& y\neq{-x}\\0 & \mbox{si}& y=-x\end{matrix}$

$\displaystyle f_y=\begin{Bmatrix} 2(x+y)\sen(\displaystyle\frac{\pi}{x+y})-\pi\cos(\displaystyle\frac{\pi}{x+y}) & \mbox{ si }& y\neq{-x}\\0 & \mbox{si}& y=-x\end{matrix}$

And here is the deal. As you see, I've calculated by definition that for all points of the form $\displaystyle (x_0,-x_0)$ 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.