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A question about mixed partial derivative

  1. Mar 25, 2003 #1
    Let there be a function f[x,y]: RxR->R

    Is there any connection between the differentiability
    (I am not sure that this is the right English term - I meant f[x,y]= a*dx+b*dy +something of smaller order)
    and the equality fxy=fyx, where fxy means the derivative of f[x,y] first by y, and than by x ?
     
  2. jcsd
  3. Mar 25, 2003 #2

    selfAdjoint

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    The idicated cross partials have to exist of course. Usually you wouls ensure that by requiring that f be twice differentiable in both variables.
     
  4. Mar 25, 2003 #3
    Thanks for the reply.

    Does that mean that double differentiability implies the fxy=fyx equality?(Or reverse plus continuity of other partial derivatives?)
     
  5. Mar 25, 2003 #4

    selfAdjoint

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  6. Mar 26, 2003 #5
    Thanks again!
    This really clarifies some things...
     
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