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Partial derivative problem

  1. Jan 31, 2009 #1
    If given an implicit function f(x,y,z)=0. Then, we can get z=g(x,y) and x= h(y,z).
    I know the answer for the partial derivative of g(x,y)' for x, how can I know the partial derivative of h(y,z) for z?

    I know f( x, y, z)=0. And I know ∂g / ∂x is positive.
    How can I define whether ∂h / ∂z is negative or positive?
    How can I express ∂h / ∂z in terms of ∂g / ∂x?
  2. jcsd
  3. Feb 1, 2009 #2


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    Hi cruxcriticoru, welcome to PF.

    Probably your answer involves the chain rule. You know that ∂g / ∂x = ∂z / ∂x is positive. Can you relate ∂h / ∂z with ∂z / ∂x using the chain rule?
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