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

Mar 1, 2016

$g ' \left(x\right) = 3 {x}^{2} + 8 x - 2$

#### Explanation:

The product rule states that

$\frac{d}{\mathrm{dx}} \left(f \left(x\right) h \left(x\right)\right) = h \left(x\right) f ' \left(x\right) + f \left(x\right) h ' \left(x\right)$

Here, the two functions being multiplied by one another are:

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

We can find each of their derivatives through the power rule.

$f ' \left(x\right) = 1$
$h ' \left(x\right) = 2 x$

Plugging these into the original expression, we see that

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

$g ' \left(x\right) = {x}^{2} - 2 + 2 {x}^{2} + 8 x$

$g ' \left(x\right) = 3 {x}^{2} + 8 x - 2$