Using sum difference derivative instead of prodict rule?

[Nano-Passion]

Main Question or Discussion Point

Let us say we have this:

$$f(x)=(x^3-x)(x^2+2)(x^2+x-1)$$

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]

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

 

[HallsofIvy]

Since you are talking about the derivative, I see no reason to multiply it out at all:
(fgh)'= fgh'+ fg'h+ f'gh.
$$((x^3−x)(x^2+2)(x^2+x−1))'= (x^3- x)(x^2+2)(2x+1)+ (x^3-x)(2x)(x^2+X-1)+ (3x-1)(x^2+2)(x^2+x-1)$$

 

[Nano-Passion]

Since you are talking about the derivative, I see no reason to multiply it out at all:
(fgh)'= fgh'+ fg'h+ f'gh.
$$((x^3−x)(x^2+2)(x^2+x−1))'= (x^3- x)(x^2+2)(2x+1)+ (x^3-x)(2x)(x^2+X-1)+ (3x-1)(x^2+2)(x^2+x-1)$$

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. :)