I'm trying to find a Taylor approximation of $ f(x) =-\frac{1}{x} \ln\left(1 + \frac{(e^{-xu}-1) (e^{-xv}-1)}{e^{-x}-1} \right) $ at $x = 0$. 

For the derivation part [Wolfram](http://www.wolframalpha.com/input/?i=d+(+-1%2Fx+*+ln(1+%2B+(e%5E(-x*u)-1)*+(e%5E(-x*y)-1)%2F(e%5E(-x)-1+))+)%2Fdx) returns a quite a tedious expression to the problem, taking the limit of which does result in the answer I'm looking for. 

As I found this problem in a textbook which is not focused on honing derivation/approximation skills, I'm curious, whether there are some known tricks that would help easying up the calculation, or is this just a technical exercise?

Apologies if this is a dumb question.