Question

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

Answer 1

`f'(x)=24x^2+4-1`

Explanation:

According to the product rule:

`f'(x)=(2x^2+x)color(blue)(d/dx[4x-1])+(4x-1)color(red)(d/dx[2x^2+x])`

Find each derivative.

`f'(x)=(2x^2+x)color(blue)((4))+(4x-1)color(red)((4x+1)`

`f'(x)=8x^2+4x+16x^2-1`

`f'(x)=24x^2+4-1`