Using sum difference derivative instead of prodict rule?

  • #1
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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
lurflurf
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Either way will work. Just guess what is most simple and start in.
 
  • #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]
 
  • #4
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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]
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.

Either way will work. Just guess what is most simple and start in.
Okay, never hurts to be completely sure. :)
 

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