Question

How do you differentiate `g(x) = (x^2+1) (x-3)^3` using the product rule?

Answer 1

`g'(x) = (x-3)^2(5x^2-6x+3)`

Explanation:

`g(x) = (x^2+1)(x-3)^3`

`g'(x) = (2x)(x-3)^3 + (x^2+1)3(x-3)^2`

`g'(x) = (x-3)^2(2x^2-6x+3x^2+3)`

`g'(x) = (x-3)^2(5x^2-6x+3)`