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Implicit partial differentiation

  1. Feb 9, 2010 #1
    I have a function z=f(xz+y) and I want to find the partial differential of z with respect to y (it's a general sort of question, I only need it in terms of the variables already given).
    My answer would be just partial df/dy but this isn't the right answer. I'm not too hot on partial differentiation so can anyone give me a hint?
  2. jcsd
  3. Feb 9, 2010 #2


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    f is apparently a function of a single variable and z is a function of x and y. Since z is not solved for, you must differentiate implicitly. So begin by taking the partial derivative of both sides with respect to y. So you will start like this:

    zy = fy(xz+y)

    Now you must use the chain rule on the right side, remembering that in the argument of f, both y and z depend on y:

    fy(xz+y) = f'(xz+y)(xz+y)y

    Now finish executing the y partials and solve for zy.
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