How do you find the derivative of ##y=ln(5x)##?

Here's the rule for deriving natural logs, which is a specific case of the chain rule:

##d/dx ln( f(x) ) = (f'(x))/f(x)##

So if we let ##f(x)## from the example above be ##5x##, you get this:

##d/dx ln( 5x ) = (5)/(5x)##

Which simplifies to ##1/x##.