# Using sum difference derivative instead of prodict rule?

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
$$((x^3−x)(x^2+2)(x^2+x−1))'= (x^3- x)(x^2+2)(2x+1)+ (x^3-x)(2x)(x^2+X-1)+ (3x-1)(x^2+2)(x^2+x-1)$$
$$((x^3−x)(x^2+2)(x^2+x−1))'= (x^3- x)(x^2+2)(2x+1)+ (x^3-x)(2x)(x^2+X-1)+ (3x-1)(x^2+2)(x^2+x-1)$$