Partial Differentiation Identity Problem

[physic]

Homework Statement

Show that a relation of the kind ƒ(x,y,z) = 0
then implies the relation
(∂x/∂y)_z (∂y/∂z)_x (∂z/∂x)_y = -1

Homework Equations

f(x,y)

df = (∂f/∂x)_y dx + (∂f/∂y)_x dy

The Attempt at a Solution

I expressed x = x(y,z) and y = y(x,z) then found dx and dy, also tried z = z(x,y) and found dz.

not sure where to go from here.

Thanks in advance

 

[Gamma]

After finding dx, dy, and dz as you described, try eliminating dx, dy and dz to find an expression that has only partial derivatives. You should be able to prove this.

Also do you know what is (partial x/partial y)_z * (partial y/ partial x)_z ? Can you verify this is equal to 1?