Question

How do you differentiate `g(x) = (2x^2 + 4x - 3) ( 2x + 2)` using the product rule?

Answer 1

`2(2x^2+4x-3) + 8(x+1)^2`

Explanation:

differentiate using the`color(blue) " Product rule "`

If `g(x) = f(x)*h(x)`, then `g'(x) = f(x)*h'(x) + h(x)*f'(x)`

let `f(x) =2x^2+4x-3`

`rArr f'(x) = 4x+4 = 4(x+1)`

and let `h(x) = 2x+2 rArr h'(x) = 2`

substitute values back into `g'(x)`

hence `g'(x) = [(2x^2+4x-3)*2 ] + [(2x+2)*4(x+1)]`

`rArr g'(x) = 2(2x^2+4x-3) + 2(x+1)*4(x+1)`

`= 2(2x^2+4x-3) + 8(x+1)^2`

If you like, this can be simplified into a single polynomial expression:

`g'(x)=12x^2+24x+2`