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

Feb 17, 2017

$f ' \left(x\right) = 10 \left(5 x - 4\right)$

#### Explanation:

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

Chain Rule: $f ' \left(x\right) = f \left(g \left(x\right)\right) g ' \left(x\right)$
here $f \left(x\right) = {x}^{2}$ and $g \left(x\right) = 5 x - 4$

$f ' \left(x\right) = 2 {\left(5 x - 4\right)}^{2 - 1} \left(5 - 0\right)$
$f ' \left(x\right) = 10 \left(5 x - 4\right)$