# Simple Partial Derivatives

• Dec 21st 2010, 05:04 PM
deanmc16
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.

$\displaystyle \frac{\partial y}{\partial x}[1-z-x]=-1$