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Homework Help: Partial Differentiation Confusion

  1. Jan 5, 2010 #1
    1. The problem statement, all variables and given/known data
    Find [tex]\frac{\partial z}{\partial x} \frac{\partial z}{\partial y} [/tex] where [tex]z=\left( [x+y]^3-4y^2 \right)^{\frac{1}{2}}[/tex]

    2. Relevant equations

    3. The attempt at a solution
    I know that [tex]\frac{\partial z}{\partial y}=\frac{3(x+y)^2-8y}{2\sqrt{(x+y)^3-4y^2}}[/tex]
    but I am unsure whether [tex]\frac{\partial z}{\partial x}[/tex] is the exact same or does not include the '-8y' in the numerator.

    I get the feeling that when finding the derivative inside the square root (in z) that y should still be treated as constant and therefore have no -8y.
    Last edited: Jan 5, 2010
  2. jcsd
  3. Jan 5, 2010 #2


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    Welcome to PF!

    Hi RazerM! Welcome to PF! :smile:

    (on this forum, you need to type "tex", not "TEX" :wink:)
    Yes, that's completely correct.

    ∂z/∂x means "keeping y constant", so that's exactly what you do! :smile:
  4. Jan 5, 2010 #3
    Re: Welcome to PF!

    So that means [tex]\frac{\partial z}{\partial x}=\frac{3(x+y)^2}{2\sqrt{(x+y)^3-4y^2}}[/tex]?
  5. Jan 5, 2010 #4


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    Yup! :biggrin:

    (nice LaTeX, btw :wink:)
  6. Jan 5, 2010 #5
    Thanks :)

    I taught myself to use LaTeX to help me with my Physics Investigation as part of Advanced Higher Physics (Highest level of physics taught in school - Scotland), we never got told to use it but no way was I using MS Office or Openoffice's limited equation typesetting, would have been a nightmare :P
  7. Jan 5, 2010 #6


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    One of the many benefits of PF membership is that you can now use LaTeX as much as you like! :biggrin:

    (in case you haven't found anything similar, a useful bookmark is http://www.physics.udel.edu/~dubois/lshort2e/node61.html#SECTION008100000000000000000" [Broken] :wink:)
    Last edited by a moderator: May 4, 2017
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