It seems like \'select count(*) from c\' in the SQL queries allowed by documentdb in the azure site and through the documentdb explorer (https://studiodocumentdb.codeplex.com/)
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")