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Differential Operators

  1. Sep 3, 2005 #1
    We're doing differential operators in my Differential Equations class right now, and our professor assigned the following problem to us:


    Which inevitably gives us the following terms as part of the final answer: Dx-xD

    The answer in the book tells me that Dx-xD = 1, and some preliminary research has told me that this is true. What I couldn't find was the why. Why, or how, does Dx-xD result in 1? And does -Dx+xD = -1?
  2. jcsd
  3. Sep 3, 2005 #2


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    product rule gives
    might be easier to see with a function
  4. Sep 3, 2005 #3
    That is because
    Hence Dx-xD=1
  5. Sep 3, 2005 #4
    Thanks! o:)
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