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Implicit function theorem proof question

  1. Dec 15, 2016 #1
    1. The problem statement, all variables and given/known data
    I understand the proof of the implicit function theorem up to the point in which I have included a photo. This portion serves to prove the familiar equation for the implicit solution f(x,y) of F(x,y,z)=c. My confusion arises between equations 8.1-4 and 8.1-5 when it is stated to "consider F as a function of x and z only." Why is this at all plausible?

    2. Relevant equations


    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Dec 15, 2016 #2
    Pardon me, I meant partial derivative fx of the implicit solution f(x,y) of F(x,y,z).
     
  4. Dec 15, 2016 #3

    Ray Vickson

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    Your image is much too small and is quite fuzzy---basically unreadable. Please type out the relevant line or two that contains your actual question.
     
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