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Implicit 'higher' differentiation

  1. Jun 29, 2008 #1
    I'm working on a cal III problem involving implicit differentiation.
    I have to find the second order partial derivative of an implicit function, basically:

    now, I know that for a single order [tex]\partial[/tex]f/[tex]\partial[/tex]x, I would simply use the chain rule property:
    [tex]\partial[/tex]f = -[tex]\partial[/tex]F/[tex]\partial[/tex]x
    [tex]\partial[/tex]x ... [tex]\partial[/tex]F/[tex]\partial[/tex]f

    But now, how would I find
    for an implicit equation?
    Last edited: Jun 29, 2008
  2. jcsd
  3. Jun 29, 2008 #2


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    Homework Helper

    What is the implicit function you are given?
  4. Jun 30, 2008 #3


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    Do the same thing again. For example, if the function were z, given by 3xz+ yez= 1, then the partial derivative, with respect to x, would be given by 3z+ 3xzx+ yezzx= 0.

    Differentiating that a second time, with respect to x, 3zx+ 3zx+ 3xzxx+ yez(zx)2+ yezzxx= 0.

    You can solve that for zxx in terms of x, y, z, and zx.
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