Implicitly differentiating PDE (multivariable calculus)

1. Nov 11, 2008

Legion81

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. Nov 11, 2008

Frillth

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?

3. Nov 11, 2008

Legion81

That's right because you have the 3z2x(dz/dx) + z3(dx/dx). I don't know what I was thinking... Thank You!

4. Nov 11, 2008

ducnguyen2000

You didn't apply the chain rule, remember df(u)/dx = f(u)'*du/dx