Earlier I asked a question about differentiating $f(x,y)$ with respect to $x-y$. I am working on the solutions trying to use the hints from earlier questions.
Is it correct to do the following: Define $u = x-y$ and $v = x + y$. Rewrite $f(x,y)$ as $g(u,v)$. Now, I understand that taking partial of $g(u,v)$ wrt $u$ is not enough because it keeps $v$ fixed, but my goal is to find how does $f$ change when $x-y$ changes without other restrictions. Can I then take total differential of $g(u,v)$ to answer that?