# Statistical Mechanics: Partial derivative with fixed variable

1. Sep 21, 2011

### steve233

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.

Thanks.

2. Sep 22, 2011

### dynamicsolo

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.