# Using sum difference derivative instead of prodict rule?

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

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

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. :)