Finding the Implicit Partial Derivative (∂y/∂x)z for x3 + y3 + z3 - 3xyz = 6

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Homework Statement



x3 + y3 + z3 - 3xyz = 6

Find (∂y/∂x)z.

Homework Equations





3. The Attempt at a Solution [/

can i simply take the partial derivative of both sides treating z as constant?

x3 + y3 + z3 - 3xyz - 6 = 0

f(x,y,z) = 0

(∂f/∂x)z = 0
 
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Yes.
 
That z is to be held constant and y thought of as a function of x only is precisely what that subscript "z" means.
 

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