I have a project using derby and JPA. I can connect to the database fine within my application. I would like to connect to the embedded database with SQL Developer so I can
SQL Developer does not support Apache Derby. It only supports a very limited (and fixed) set of DBMS as documented on the WebSite:
(All third party DBMS are listed as "read-only" on the website - whatever that means)
You will need a "real" general purpose JDBC client to use it against Derby like Squirrel, DbVisualizer or SQL Workbench/J.