Daily and Differential Backups
If you're using MySQL with InnoDB tables, then you could take incremental backups with Percona's xtrabackup, or talk to Oracle about enterprise licensing, which would net you MySQL Enterprise Backup.

Xtrabackup is a brilliant piece of software, but it behaves very differently from traditional MySQL backups using mysqldump, and it's worth spending some time studying and testing it before you look at rolling it into production.

If you're using MySQL with MyISAM, you're pretty much out of luck. You could perhaps do something logically, like maintain "last modified" timestamps on your tables that are maintained by triggers, but there's manual maintenance and several caveats that might make that unwise.

Recent versions of Xtrabackup should also work with MariaDB, though again you'll probably want to test this yourself.