I am slightly confused by a problem I have been given, namely:
$$-\frac{d}{dx}\ln(Y(x))$$ with $$Y(x)=\prod_{i=1}^{\infty}(1+e^{-xa_i})$$.
Now I have alredy looked at what the infinite product will turn into, which I think will be $1$ plus a sum of all possible subsets of and including $\prod_{i=1}^{\infty}e^{-xa_i}$, but I am not sure how I should derive this inner part. Is my approach too complicated?