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Chain rule for second derivatives

  1. Sep 13, 2007 #1
    1. The problem statement, all variables and given/known data
    I cannot believe I do not know this!

    [tex] dx/dt = dx/dt' dt'/dt [/tex] is the chain rule for first derivatives

    [tex] d^2x/dt^2 = ? [/tex] is the chain rule for second derivatives

    if it is complicated could you link me to a source that explains it please

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 13, 2007 #2

    Hurkyl

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    What's the problem with differentiating the first derivative?
     
  4. Sep 13, 2007 #3
    [tex] d^2x/dt^2 = d^2x/(dt'dt) dt'/dt + dx/dt d^2t'/dt^2 [/tex]?

    The product rule was used. That mixed partial seems out of place. Is the above correct?
     
  5. Sep 14, 2007 #4

    HallsofIvy

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    What makes you think there is a "chain rule for second derivatives"?
     
  6. Sep 14, 2007 #5
    Well, is there something wrong with what I posted? Maybe I just discovered it.
     
  7. Sep 14, 2007 #6

    Hurkyl

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    Looks right. If you don't want the mixed partial, then why not apply the chain rule? After all, dx/dt' is merely a function... (Call it y, if you're having trouble thinking about it)
     
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