Question

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

Answer 1

`f'(x)=16x^3-9x^2+16x+2`

Explanation:

According to the product rule:

`f'(x)=(x^3+2x+2)color(blue)(d/dx[4x-3])+(4x-3)color(red)(d/dx[x^3+2x+2]`

Find each derivative.

`f'(x)=(x^3+2x+2)color(blue)((4))+(4x-3)color(red)((3x^2+2))`

`f'(x)=4x^3+8x+8+12x^3+8x-9x^2-6`

`f'(x)=16x^3-9x^2+16x+2`