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Does differential order matter?

  1. Sep 3, 2011 #1
    is this the same? why are they the same? do the order of differential not matter?

    d/dxi (dyj / dxj) = d/dxj (dyj / dxi)

    where LHS : differentiate yj w.r.t xj first, then xi

    while RHS: differentiate yj w.r.t xi first, then xj

    thanks!
     
  2. jcsd
  3. Sep 4, 2011 #2

    HallsofIvy

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    As long as f and its first and second derivatives are continuous, in some neighborhood of a point, the "mixed" derivatives
    [tex]\frac{\partial f}{\partial x\partial y}[/tex]
    and
    [tex]\frac{\partial f}{\partial y\partial x}[/tex]
    are equal at that point.
     
  4. Sep 6, 2011 #3
    is this a total differential function? or is it just a normal differential property?

    i seem to be mixing everything up :(
     
  5. Sep 6, 2011 #4

    HallsofIvy

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    I have no idea what you are asking. I don't know what you mean by "total differential function" (I do know what a total differential is) or 'normal differential property".

    There is no "total differential" in this problem. It is entirely a property of partial derivatives.
     
  6. Sep 7, 2011 #5
    ah i see than kyou
     
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