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Partial derivatives

  1. Feb 28, 2012 #1
    1. The problem statement, all variables and given/known data

    I dont understand why

    ∂f/∂x = xy = y


    ∂f/∂x = x2 + y2 = 2x

    Why does the y disappear in the second but not in the first?
  2. jcsd
  3. Feb 28, 2012 #2


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    Homework Helper

    hi bobsmith76! :wink:

    you mean? …
    ∂/∂x (xy) = y

    ∂/∂x (x2 + y2) = 2x​

    in each case, y is treated as a constant

    in the first, it's multiplied, so it stays; in the second, it's on its own, so its derivative is zero :smile:

    ∂/∂x means differentiating wrt x while keeping all other variables constant
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