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Find the value of dz/dx at the point (1,1,1) if the equation xy+z^{3}x-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 z^{3}x part. I thought you would use the product rule and get 3(dz/dx)^{2}x + z^{3}. But if that is right, the final equation looks something like

y + 3x(dz/dx)^{2}+ z^{3}- 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

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# Homework Help: Implicitly differentiating PDE (multivariable calculus)

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