Mathematical Thermal Physics Problem

[Elzair]

Homework Statement

Suppose there exists a relation among three coordinates x, y and z such that

$$f(x,y,z) = 0$$

Then prove the following relation

Homework Equations

$$\left(\frac{\delta x}{\delta y} \right)_{z} = \frac{1}{\left( \frac{\delta y}{\delta x} \right)_{z}}$$

The Attempt at a Solution

I am not sure how to go about this one. Any suggestions?

 

[Shooting Star]

If z is constant, then the partial derivative of x wrt y = dx/dy, and the partial derivative of y wrt x is dy/dx. There is a well known property, (for well behaved functions), that dy/dx = 1/(dx/dy), which is what you have to show.