# How do you use the chain rule to differentiate y=(x+2)^4?

Jan 14, 2018

$4 {\left(x + 2\right)}^{3}$

#### Explanation:

by chain rule, $\frac{d}{\mathrm{dx}} \left(f \left(g \left(x\right)\right)\right) = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$

for this problem,
$f \left(x\right) = {x}^{4} \mathmr{and} g \left(x\right) = x + 2$
$f ' \left(x\right) = 4 {x}^{3} \mathmr{and} g ' \left(x\right) = 1$

that means $\frac{d}{\mathrm{dx}} {\left(x + 2\right)}^{4} = 4 {\left(x + 2\right)}^{3} \cdot 1 = 4 {\left(x + 2\right)}^{3}$