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

Dec 31, 2015

$f ' \left(x\right) = 18 {x}^{2} - 12 x + 3$

#### Explanation:

The product rule states that for some function

$f \left(x\right) = g \left(x\right) h \left(x\right) , f ' \left(x\right) = g ' \left(x\right) h \left(x\right) + h ' \left(x\right) g \left(x\right)$

Here, we have

$\left\{\begin{matrix}g \left(x\right) = 2 {x}^{2} + 1 \\ h \left(x\right) = 3 x - 3\end{matrix}\right.$

Differentiate each function.

$\left\{\begin{matrix}g ' \left(x\right) = 4 x \\ h ' \left(x\right) = 3\end{matrix}\right.$

Relate these to find $f ' \left(x\right)$.

$f ' \left(x\right) = 4 x \left(3 x - 3\right) + 3 \left(2 {x}^{2} + 1\right)$

Distribute and simplify.

$f ' \left(x\right) = 18 {x}^{2} - 12 x + 3$