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Analyze two variable function with respect to another function

  1. Dec 19, 2012 #1
    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?
  2. jcsd
  3. Dec 19, 2012 #2


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    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.
  4. Dec 19, 2012 #3
    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?
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