Final answer:
Dynamic routing utilizes a routing protocol to automatically find and update paths in the routing tables of routers, adapting to changes in network topology.
Step-by-step explanation:
Dynamic routing utilizes a routing protocol to find and update routing tables on a router. This method allows routers to automatically discover and maintain awareness of the network paths. As network topology changes, a dynamic routing protocol can adapt by recalculating routes and updating routing table entries with new best paths. Protocols such as Open Shortest Path First (OSPF), Border Gateway Protocol (BGP), and Enhanced Interior Gateway Routing Protocol (EIGRP) are examples of routing protocols that manage dynamic routing in various types of networks.