# How do you differentiate  f(x)=(6x-4)(6x+1)^3  using the product rule?

$f ' \left(x\right) = 6 {\left(6 x + 1\right)}^{2} \left(24 x - 11\right)$

#### Explanation:

$f \left(x\right) = \left(6 x - 4\right) {\left(6 x + 1\right)}^{3}$
$f ' \left(x\right) = \left(6 x - 4\right) \cdot 3 {\left(6 x + 1\right)}^{3} \cdot 6 + {\left(6 x + 1\right)}^{3} \cdot 6$
$f ' \left(x\right) = 6 {\left(6 x + 1\right)}^{2} \left(3 \cdot \left(6 x - 4\right) + 6 x + 1\right)$
$f ' \left(x\right) = 6 {\left(6 x + 1\right)}^{2} \left(18 x - 12 + 6 x + 1\right)$
$f ' \left(x\right) = 6 {\left(6 x + 1\right)}^{2} \left(24 x - 11\right)$