# Mathematical Thermal Physics Problem

1. Jan 24, 2008

### Elzair

1. The problem statement, all variables and given/known data
Suppose there exists a relation among three coordinates x, y and z such that

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

Then prove the following relation

2. Relevant equations

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

3. The attempt at a solution
I am not sure how to go about this one. Any suggestions?

2. Jan 25, 2008

### 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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook