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Chain rule with 2nd Partials

  1. Oct 11, 2009 #1
    We have f(x(y,z),t(y,z)).

    This is more of a study question. I don't know how to expand out [tex]d^{2}f/dz^2[/tex]


    I know df/dz = df/dx*dx/dz + df/dt*dt/dz, but I don't know how to expand this to the 2nd derivative. I think the product rule comes in to play? Not really sure.

    Thanks for your help.
     
  2. jcsd
  3. Oct 11, 2009 #2

    LCKurtz

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    Using the more convenient subscript notation, you have used:

    fz = fxxz+ fttz

    Now you have to do the same thing to this expression, which can be done termwise:

    fzz =(fxxz)x[itex]\cdot\, [/itex]xz + (fxxz)t[itex]\cdot\, [/itex]tz

    and, yes, you will need the product rule inside those parentheses.
     
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