Whenever possible, rewrite a function so it looks good before taking its derivative.
Any logarithm logb a can be written as
This allows us to find derivatives of logarithms in bases besides e.
We also know enough now to find derivatives of things like
f(x) = ln (x2).
We can bring down the exponent to find
f(x) = 2ln x,
and we know how to find the derivative of this: