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Partial Derivative Question

  1. Jul 29, 2011 #1
    For the equation:

    h(x,y,z)=y/(x+y+z)

    using quotient rule:

    f(y)=y
    g(x,y,z)=x+y+z

    hy = (x+y+z)(1)-(y)(1) / (x+y+z)2
    = x+z / (x+y+z)2

    I am getting the correct answer when evaluating at a point, but is this differentiation correct?

    More specifically, when using the quotient rule for partial derivatives, is it correct to differentiate f and g with respect to y, and then apply the quotient rule? Is this method generally correct?
     
  2. jcsd
  3. Jul 29, 2011 #2

    Dick

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    Science Advisor
    Homework Helper

    You are doing just fine. Yes, it is generally correct.
     
  4. Jul 30, 2011 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The partial derivative is just the ordinary derivative with the other variables treated like constants. All ordinary derivative laws apply to partial derivatives.
     
  5. Jul 30, 2011 #4
    Great, thanks for your help.
     
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