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

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SUMMARY

The discussion centers on the application of implicit differentiation as a method to transition from equation (4) to equation (5) in a specific mathematical paper. The author initially struggled to replicate the move but successfully resolved the issue shortly after posting. The relevant paper can be accessed via JSTOR, and a visual reference is provided through an image link. This highlights the importance of understanding implicit differentiation in mathematical proofs.

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

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