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Multi variable partial differentiation, cant solve

  1. Feb 15, 2010 #1
    1. The problem statement, all variables and given/known data

    If z = f(x-y), show that dz/dx + dz/dy = 0

    2. The attempt at a solution
    I thought:

    dz/dx = fx
    dz/dy = -fy

    which doesnt make sense really... because its not equal to 0.

    or maybe it should be:
    dz/dx = dz/df * df/dx = fx * ??
    dz/dy = dz/df * df/dy = -fy * ??
     
  2. jcsd
  3. Feb 15, 2010 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Use the chain rule. If z= f(u) and u= x- y then [itex]\partial f/\partial x= df/du \partial u/\partial x[/itex] and [itex]\partial f/\partial y= df/du \partial u/\partial y[/itex].

    (If z= f, then "dz/df" is just 1.)
     
  4. Feb 15, 2010 #3
    Thats great thx.

    dz/dx = df/du du/dx = fu * 1 = fu
    dz/dy = df/du du/dy = fu * -1 = -fu


    dz/dx + dz/dy = fu - fu = 0
     
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