# How do you differentiate g(x) = (6x+9)(x^2-4) using the product rule?

Jun 6, 2018

$g ' \left(x\right) = 18 {x}^{2} + 18 x - 24$

#### Explanation:

$\text{given "g(x)=f(x)h(x)" then}$

$g ' \left(x\right) = f \left(x\right) h ' \left(x\right) + h \left(x\right) f ' \left(x\right) \leftarrow \textcolor{b l u e}{\text{product rule}}$

$f \left(x\right) = 6 x + 9 \Rightarrow f ' \left(x\right) = 6$

$h \left(x\right) = {x}^{2} - 4 \Rightarrow h ' \left(x\right) = 2 x$

$\Rightarrow g ' \left(x\right) = 2 x \left(6 x + 9\right) + 6 \left({x}^{2} - 4\right)$

$\textcolor{w h i t e}{\Rightarrow g ' \left(x\right)} = 12 {x}^{2} + 18 x + 6 {x}^{2} - 24$

$\textcolor{w h i t e}{\Rightarrow g ' \left(x\right)} = 18 {x}^{2} + 18 x - 24$