My problem is getting that derivative. I've only found the derivative of simple natural logs like ln(x) where I can just differentiate to 1/x.
It could be that you are simply not ready to do this question.
In that case you need to have a sit down one to one with an tutor.
We here do not provide that service.
The purpose of logarithmic differentiation is to make use of logarithm rules to simplify the function, so that difficult functions can be differentiated more easily.