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Partial derivative equals zero means it is constant?

  1. Aug 14, 2011 #1
    Suppose we have a function

    [tex]u=f(x,y,z)[/tex]

    If [tex]\frac{\partial u}{\partial x} = 0[/tex]

    then u is independent of x and is
    [tex]u=f(y,z)[/tex]
    only.

    Correct?
     
  2. jcsd
  3. Aug 14, 2011 #2

    gb7nash

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    Homework Helper

    Correct. Think about it. If [itex]\frac{\partial u}{\partial x} = 0[/itex], this means that the value of u does not change whenever x changes. i.e. u does not depend on x.
     
  4. Aug 14, 2011 #3

    Stephen Tashi

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    Science Advisor


    It's interesting to contemplate the distinction between saying "u does not depend on x" and "u is not a function of x". For example, in the case of a single variable, the function that maps all real numbers to 3, which we write as f(x) = 3, is a constant function. But some people say it is "not a function of x" when they mean it "does not depend on x".
     
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