Get record count in Azure DocumentDb
This is now possible in the year 2017 of our lord.
SELECT VALUE COUNT(1) FROM c
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Until the implementation of the "count" keyword, you should do your query in a store procedure on the server. Take care to not get all columns/properties in your query if you want only a count.
Select only the id like;
dc.CreateDocumentQuery(update.SelfLink, "SELECT c.id FROM c")