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Partial Differentiation Identity Problem

  1. Jan 22, 2014 #1
    1. The problem statement, all variables and given/known data
    Show that a relation of the kind ƒ(x,y,z) = 0
    then implies the relation
    (∂x/∂y)_z (∂y/∂z)_x (∂z/∂x)_y = -1


    2. Relevant equations

    f(x,y)

    df = (∂f/∂x)_y dx + (∂f/∂y)_x dy



    3. The attempt at a solution

    I expressed x = x(y,z) and y = y(x,z) then found dx and dy, also tried z = z(x,y) and found dz.

    not sure where to go from here.

    Thanks in advance
     
  2. jcsd
  3. Jan 22, 2014 #2
    After finding dx, dy, and dz as you described, try eliminating dx, dy and dz to find an expression that has only partial derivatives. You should be able to prove this.

    Also do you know what is (partial x/partial y)_z * (partial y/ partial x)_z ? Can you verify this is equal to 1?
     
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