# How do you differentiate f(x)=(3x+2)(2x^2-5x+1)  using the product rule?

Jan 9, 2016

I found $f ' \left(x\right) = 18 {x}^{2} - 22 x - 7$

#### Explanation:

Let us consider the Product Rule:

apply it to our case:

$f ' \left(x\right) = 3 \left(2 {x}^{2} - 5 x + 1\right) + \left(3 x + 2\right) \left(4 x - 5\right) =$
$= 6 {x}^{2} - 15 x + 3 + 12 {x}^{2} - 15 x + 8 x - 10 =$
$= 18 {x}^{2} - 22 x - 7$