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Homework Help: Statistical Mechanics: Partial derivative with fixed variable

  1. Sep 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Given y = xz5 and x = zg find :

    (∂y / ∂x)z
    (∂y / ∂x)g

    2. Relevant equations
    3. The attempt at a solution

    I understand the concept of a partial derivative, but I've never seen one such that there is a variable held fixed, or one where ∂x is not changing independently. Any tips on how to do this?

    My solution is basically treat z as a constant but that would be the same as taking the partial without holding z constant. I'm not sure what to do about x either. Just need an example of or instruction on how to do this.

  2. jcsd
  3. Sep 22, 2011 #2


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    Homework Helper

    I think that is all they want for the first one. I suspect the notation is being used this way so that for the second one, you would replace z by substitution and again differentiate with respect to x, holding g fixed.
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