# How do you differentiate  y =4x ln(3x + 2) using the chain rule?

Mar 19, 2017

$\ln \left(x + 2\right) + \frac{x}{x + 2}$

#### Explanation:

It is not the chain rule, but the product rule which would apply here first. Accordingly,

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left(x\right) \ln \left(3 x + 2\right) + x \frac{d}{\mathrm{dx}} \ln \left(x + 2\right)$... application of product rule.

=$\ln \left(x + 2\right) + \frac{x}{x + 2} \frac{d}{\mathrm{dx}} \left(x + 2\right)$.... application of chain rule.

= $\ln \left(x + 2\right) + \frac{x}{x + 2}$