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Higher Order Partial Derivatives and Clairaut's Theorem

  1. Feb 23, 2013 #1
    1. The problem statement, all variables and given/known data
    general course question


    2. Relevant equations
    N/A


    3. The attempt at a solution
    fx is a first order partial derivative
    fxy is a second order partial derivative
    fxyz is a third order partial derivative

    I understand that Clairaut's Theorem applies to second order derivatives, does it also apply to higher partial derivatives though?

    Example:
    fxy=fyx (Clairaut's)

    So does this apply?
    fxyz=fxzy=fzyx
     
  2. jcsd
  3. Feb 23, 2013 #2
    Yes it applies.
    (1) fxy=fyx (Clairaut's)
    We know that:
    fxyz=(fx)yz
    How can you prove that:
    fxyz=fxzy using that?
     
    Last edited: Feb 23, 2013
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