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Implicitly differentiating PDE (multivariable calculus)

  1. Nov 11, 2008 #1
    The problem:
    Find the value of dz/dx at the point (1,1,1) if the equation xy+z3x-2yz=0 defines z as a function of the two independent variables x and y and the partial derivative exists.

    I don't know how to approach the z3x part. I thought you would use the product rule and get 3(dz/dx)2x + z3. But if that is right, the final equation looks something like

    y + 3x(dz/dx)2 + z3 - 2y(dz/dx) = 0

    And I don't think that is right. The only way I know to solve that would be with the quadratic equation and that gives a complex value. Am I forgeting the chain rule somewhere or just way off on approaching this problem?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Nov 11, 2008 #2
    I have done very little multivariable so this could easily be wrong, but if you implicitly differentiated z^3x shouldn't you get 3z^2x*dz/dx + z^3?
  4. Nov 11, 2008 #3
    That's right because you have the 3z2x(dz/dx) + z3(dx/dx). I don't know what I was thinking... Thank You!
  5. Nov 11, 2008 #4
    You didn't apply the chain rule, remember df(u)/dx = f(u)'*du/dx
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