How does implicit differentiation explain the move from (4) to (5)?

[ruzbayhhi]

I spent a lot of time trying to understand the move the author makes in this paper from (4) to (5). It seems like it is a straightforward application of implicit differentiation, but I just can't replicate that.

Relevant segment:
http://i.imgur.com/GqFUxpQ.jpg
Relevant paper:
http://www.jstor.org/discover/10.2307/2555613?uid=2&uid=4&sid=21102852414973

 

[ruzbayhhi]

aaaannnnd five minutes after posting this I managed to solve it...