# How do you differentiate f(x) = 5(x^2-4 )^(2)  using the chain rule?

May 7, 2018

$f ' \left(x\right) = 20 x \left({x}^{2} - 4\right)$

#### Explanation:

$f \left(x\right) = 5 {\left({x}^{2} - 4\right)}^{2}$
$f ' \left(x\right) = 5 \cdot 2 \left({x}^{2} - 4\right) \cdot 2 x$
$f ' \left(x\right) = 20 x \left({x}^{2} - 4\right)$

The chain rule is given by:

$F \left(x\right) = f \left(g \left(x\right)\right)$
$F ' \left(x\right) = f ' \left(g \left(x\right)\right) \times g ' \left(x\right)$