# How do you differentiate  f(x)= (3x+2)^3  using the chain rule.?

Dec 25, 2015

$f ' \left(x\right) = 9 {\left(3 x + 2\right)}^{2}$

#### Explanation:

Use the chain rule.

In this scenario, according to the chain rule:

$\frac{d}{\mathrm{dx}} \left({u}^{3}\right) = 3 {u}^{2} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$

Thus,

$f ' \left(x\right) = 3 {\left(3 x + 2\right)}^{2} \cdot \frac{d}{\mathrm{dx}} \left(3 x + 2\right)$

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

$\implies 9 {\left(3 x + 2\right)}^{2}$