Step $2$

We will now apply the chain rule for differentiating logarithmic expressions as stated in the previous step.

$\frac{d}{dx}ln([f(x)])=\frac{1}{f(x)}{f}^{\text{'}}(x)$

Using the above to differentiate $y=\frac{1}{5}ln(3-8x)$ gives the following result.

$\frac{dy}{dx}=(\frac{1}{5})\frac{d}{dx}(ln(3-8x))$

$=x$