There is a good TechNet article about how to permit your DHCP servers to update DNS. One of the things recommended is that the list of DHCP servers be placed in the DNSUpdateProxy builtin group.
In a prior post I referred to a script that got a list of DHCP servers. I found that one to be inadequate for my needs so I rewrote it as DHCPServerList.vbs. Why do I need a script to list DHCP servers? I work in an environment with a large number of domains, and a large number of DHCP servers. Interestingly, the name of the servers is kept in the configuration container of AD. As a result, you may delete a computer object, and still have it appear as an available DHCP server. This script not only pings the servers, but also looks for the AD path to the computer object.
A logfile is written to your desktop. Rename to change .txt to .vbs.