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Math Help - Simple Partial Derivatives

  1. #1
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    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
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  2. #2
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    \displaystyle \frac{\partial y}{\partial x}[1-z-x]=-1
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