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Multivariable Chain Rule

  1. Nov 13, 2011 #1
    Suppose I have

    F(x,y) and y=y(t) and x=x(t)

    Therefore,

    Ft = Fx*xt + Fy*yt. Right?

    Can I write

    Ftt = (Fxx*xt + Fyy*yt)*xt + Fx*xtt + (Fxx*xt + Fyy*yt)*yt + Fy*ytt

    ?

    Basically I'm trying to figure out the second derivative by chain rule.
     
  2. jcsd
  3. Nov 13, 2011 #2

    Dick

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    Shouldn't there be some F_xy's and F_yx's in there?
     
  4. Nov 13, 2011 #3
    You're right. I meant to write:


    Ftt = (Fxx*xt + Fxy*yt)*xt + Fx*xtt + (Fyx*xt + Fyy*yt)*yt + Fy*ytt
     
  5. Nov 13, 2011 #4

    Dick

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    Looks ok now, good job. Just product rule and chain rule, yes?
     
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