About Derby "ERROR 42X51: The class '***' does not exist or is inaccessible. This can hap pen if the class is not public."

This link [1] contains a straight forward example to create UDF. Link [2] is the official page to explain difference between Functions and Procedures and other examples. Link [3] lists all data type can be used. Link [5] shows how to add/delete/replace the jar file.

Following is my commands in Derby ij:
call sqlj.install_jar('ed.jar', 'APP.ed',0);
call syscs_util.syscs_set_database_property('derby.database.classpath', 'APP.ed');
create function myED(first_str varchar(50), second_str varchar(50)) returns integer parameter style java no sql language java external name 'EditDistance.LD';

To solve the error, you should put the .java file inside the jar file, especially when you create the jar file using Eclipse. There is an option to do that. Detail is at link [4]. Use this command to show all installed function: “select s.schemaname, f.filename from sys.sysschemas s, sys.sysfiles f  where s.schemaid=f.schemaid; ” Also you can find a copy of the installed jar file under the sub-directory called “jar” within your the database directory.

Reference:
[1] http://www.wisteme.com/question.view?targetAction=viewQuestionTab&id=67
[2] http://wiki.apache.org/db-derby/DerbySQLroutines
[3] http://db.apache.org/derby/docs/10.2/ref/crefsqlj31068.html#crefsqlj31068
[4] http://old.nabble.com/Problems-create-SQL-Function-td23595863.html
[5] http://db.apache.org/derby/docs/10.0/manuals/develop/develop43.html