Dhcp is not dynamically updating dns
This protocol-based DNS update method was documented and standardized in IETF publication RFC 2136 in 1997 and has become a standard part of the DNS protocol (see also nsupdate program).The explosive growth and proliferation of the Internet into homes brought a growing shortage of available IP addresses.
Today, numerous providers, called Dynamic DNS service providers, offer such technology and services on the Internet.
Dynamic DNS (DDNS or Dyn DNS) is a method of automatically updating a name server in the Domain Name System (DNS), often in real time, with the active DDNS configuration of its configured hostnames, addresses or other information.
The term is used to describe two different concepts.
Smaller services, however, are generally much more likely to move from host to host over shorter periods of time.
Servers being run on certain types of Internet service provider, cable modems in particular, are likely to change their IP address over very short periods of time, on the order of days or hours.