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Partial Differentiation (very simple mistake, I think!)

  1. Apr 15, 2010 #1
    1. The problem statement, all variables and given/known data
    [PLAIN]http://img408.imageshack.us/img408/7163/partialdifferent.jpg [Broken]

    So this means differentiate w.r.t y first, so I want dz/dy, and then w.r.t x right?

    so I rearrange so that y=z3/3 + xz
    and differentiate w.r.t z to get dy/dz, and then do 1 over this which i get as:


    and then differentiating this w.r.t x, I get

    which isn't quite right. Can anyone see where I've gone wrong? Thanks.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 15, 2010 #2


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    You need to use the chain rule. Don't forget z still varies with x.
  4. Apr 15, 2010 #3
    It may help to rewrite [itex]z[/itex] as [itex]z(x,y)[/itex] -- looks clunkier, but I find that it helps me remember that I have multivariate function.
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