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Mathematical Thermal Physics Problem

  1. Jan 24, 2008 #1
    1. The problem statement, all variables and given/known data
    Suppose there exists a relation among three coordinates x, y and z such that

    [tex]f(x,y,z) = 0[/tex]

    Then prove the following relation


    2. Relevant equations

    [tex]\left(\frac{\delta x}{\delta y} \right)_{z} = \frac{1}{\left( \frac{\delta y}{\delta x} \right)_{z}}[/tex]

    3. The attempt at a solution
    I am not sure how to go about this one. Any suggestions?
     
  2. jcsd
  3. Jan 25, 2008 #2

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    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.
     
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