Simple Partial Derivatives

Hi,

I have a problem that involves three real variables x, y and z. They are subject to the following constraints:

1. x, y, and z are all >=0

2. x+y+z=1

Other than for the above constraints, there are no other relationships between x, y and z.

My question is: What is the partial derivative of one variable with respect to another (e.g. y wrt x)?

I originally thought they would be 0. But on second thoughts you could say e.g. y = 1-x-z, so dy/dx=-1.

Thanks in advance for your help.

Dean