Analyze two variable function with respect to another function

[Essa1987]

Can you please help me with the following problem:
Given a function of the form f(x,y) = (a-b x)^2 - (c - d y)^2, how can I tell how does f change when (x-y) change?

 

[mathman]

I am not quite sure what they question is supposed to represent. However, let u = x-y and v = x+y, then change f(x,y) into g(u,v). I believe that the answer would be ∂g/∂u.

The ambiguity is that v = x+y is not the only choice possible.

 

[Essa1987]

Thank you, mathman!

I agree, I was thinking about the ambiguity as well. I could also choose v = x etc and this will lead to a different solution.

I do not understand, however, what else do I need to know about the problem to make it concrete?