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What Basic Derivative Rule Is Responsible For This?

  1. Sep 22, 2009 #1
    If:

    [tex]a(x)=b(x)-c(x)[/tex]

    Then:

    [tex]\frac{da}{dx}=\frac{db}{dx}-\frac{dc}{dx}[/tex]

    Please note that the sum/difference rule is not directly invoked since it talks about a derivative of a sum/difference being equal to the sum/difference of the derivatives. It could very well be the basis for this logic, although I don't see it offhand. And of course, this is not a homework question. I came across this logic today and was surprised I could use it.
     
    Last edited: Sep 22, 2009
  2. jcsd
  3. Sep 22, 2009 #2

    LCKurtz

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    It certainly is the sum-difference rule. When you compute a'(x) on the left you are asking for (b(x) - c(x))' on the right, which, by the difference rule is b'(x) - a'(x).
     
  4. Sep 22, 2009 #3
    Ah yes! Thank you. All I had to do was write "d(b-c)" instead of "da" and I would have seen it immediately.
     
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