# How do you differentiate f(x) = (3x+7)^5? using the chain rule?

Dec 3, 2015

$f ' \left(x\right) = 15 {\left(3 x + 7\right)}^{4}$

#### Explanation:

$f \left(x\right) = {\left(3 x + 7\right)}^{5}$

Chain rule: $f \left(g \left(x\right)\right) = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$

$f ' \left(x\right) = 5 {\left(3 x + 7\right)}^{5 - 1} \cdot \frac{d}{\mathrm{dx}} \left(3 x + 7\right)$

$= 5 {\left(3 x + 7\right)}^{4} \left(3\right)$
$= 15 {\left(3 x + 7\right)}^{4}$