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Chain Rule Proof

  1. Nov 10, 2011 #1
    1. The problem statement, all variables and given/known data
    If Z= F(x-y), show that Zx + Zy = 0


    2. Relevant equations



    3. The attempt at a solution
    Suppose I let Q = x-y. Then, by chain rule,

    Fx(Q) * 1 + Fy(Q) * -1. By identity, this statement must hold for all values x,y. In particular, it must hold for x=y. By x=y,

    Fy(Q) * 1 + Fy(Q) * -1 = 0.

    Is this legitimate?
     
  2. jcsd
  3. Nov 10, 2011 #2
    I'm not sure what you mean by Fx(Q) * 1 + Fy(Q) * -1. Are you differentiating F(Q) with respect to x and to y?
     
  4. Nov 10, 2011 #3

    Deveno

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    Science Advisor

    F is just a real-valued function, it only has one derivative.

    if Q(x,y) = x-y, then Q has 2 partials, Qx and Qy.

    using the chain rule we get:

    Zx = F'(Q)Qx

    your turn.
     
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