# How do you differentiate  f(x)=ln(6x+8) using the chain rule.?

Aug 4, 2016

$= \frac{3}{3 x + 4}$

#### Explanation:

break it up as follows

$f \left(u\right) = \ln \left(u\right)$ and $u \left(x\right) = 6 x + 8$

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{\mathrm{df}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$

$= \frac{d}{\mathrm{du}} \ln u \cdot \frac{d}{\mathrm{dx}} \left(6 x + 8\right)$

$= \frac{1}{u} \cdot 6$

$= \frac{1}{6 x + 8} \cdot 6$

$= \frac{3}{3 x + 4}$