Connecting to MySQL 5.1 using IBM Data Studio
Here is a similar processes to connect to a local derby database

Confirm that your Debrby server is running

I used the startNetworkServer.bat file on Windows 7 to start derby

Open IBM Data Studio
Navigate to Windows>Prefernces>DataManagement>Connectivity>Driver Definitions

Edit the Specific Driver you will use to connect

In my case that was Derby10.2-DerbyClient JBDC Driver Default

On the Jar List tab you will see the default driver files

In my case I updated to c:\db-derby\lib\derbyclient.jar  since my derby is installed in c:\db-derby

I had to save this new location and restart IBM Sata Studio

When I selected this connection parameter in the JDBC driver pulldown I was able to define a successful connection 

Hope this helps