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Homework Help: 3 variable derivative.

  1. Nov 11, 2008 #1
    1. The problem statement, all variables and given/known data

    Find dz/dt where z = (x^2)(t^2) and x^2 + 3xt + 2t^2 = 1.

    2. The attempt at a solution

    I really have no idea how to go about this, I've tried rearranging the second expression in terms of x but it's no help.
  2. jcsd
  3. Nov 11, 2008 #2


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    Science Advisor

    Use the impllicit differentiation.

    Differentiating the first equation, with respect to t,
    [tex]dz/dt= 2tx^2+ 2t^2x dx/dt[/tex]

    Differentiating the second equation, with respect to t,
    [tex]2x dx/dt+ 3t dx/dt+ 3x+ 4t= 0[/tex]
    [tex](2x+ 3t)dx/dt= -(3x+ 4t)[/tex]
    [tex]dx/dt= -(3x+4t)/(2x+ 3t)[/tex]
    Replace dx/dt in the first equation by that.
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