Using sum difference derivative instead of prodict rule?

Nano-Passion · Oct 29, 2011

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.

lurflurf · Oct 30, 2011

Either way will work. Just guess what is most simple and start in.

HallsofIvy · Oct 30, 2011

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]

Nano-Passion · Oct 30, 2011

HallsofIvy said: ↑

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.

lurflurf said: ↑

Either way will work. Just guess what is most simple and start in.

Okay, never hurts to be completely sure. :)

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Using sum difference derivative instead of prodict rule?

Nano-Passion

lurflurf

HallsofIvy

Nano-Passion

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