Statistical Mechanics: Partial derivative with fixed variable

[steve233]

1. Homework Statement

Given y = xz⁵ and x = zg find :

(∂y / ∂x)_z
(∂y / ∂x)_g

2. Homework 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.

 

[dynamicsolo]

Given y = xz⁵ and x = zg find :

(∂y / ∂x)_z
(∂y / ∂x)_g

My solution is basically treat z as a constant but that would be the same as taking the partial without holding z constant.

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.