Question

How do you differentiate `g(x) =(x^2 + 6) (x^2 - 2x + 1)^4` using the product rule?

Answer 1

`g(x) =(x^2 + 6) (x^2 - 2x + 1)^4`

Our task will be simpler if we note that `x^2-2x+1 = (x-1)^2`, so

`g(x) = (x^2+6)(x-1)^8`

`g'(x) = 2x(x-1)^8 + (x^2+6)*8(x-1)^7`

`= 2(x-1)^7[x(x-1)+4(x^2+6)]`

`= 2(x-1)^7(5x^2-x+24)`