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

[unscientific]

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

 

[haruspex]

Yes.

 

[HallsofIvy]

That z is to be held constant and y thought of as a function of x only is precisely what that subscript "z" means.