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Using sum difference derivative instead of prodict rule?

  1. Oct 29, 2011 #1
    Let us say we have this:

    [tex]f(x)=(x^3-x)(x^2+2)(x^2+x-1)[/tex]

    Would it be equally correct to multiply the first two binomials, and then taking that and multiplying by the last tri-nomial; and then using the sum rule? It seems perfectly fine (and much simpler!) but I want to make sure I am not violating anything here. It seems like a longer problem to use the product rule twice.
     
  2. jcsd
  3. Oct 30, 2011 #2

    lurflurf

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    Either way will work. Just guess what is most simple and start in.
     
  4. Oct 30, 2011 #3

    HallsofIvy

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    Since you are talking about the derivative, I see no reason to multiply it out at all:
    (fgh)'= fgh'+ fg'h+ f'gh.
    [tex]((x^3−x)(x^2+2)(x^2+x−1))'= (x^3- x)(x^2+2)(2x+1)+ (x^3-x)(2x)(x^2+X-1)+ (3x-1)(x^2+2)(x^2+x-1)[/tex]
     
  5. Oct 30, 2011 #4
    True, I just figured I should simplify that more, so I wanted to do the other route. But now I see you don't have to simplify that more.

    Okay, never hurts to be completely sure. :)
     
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