To take a mysql dump you should not be logged into mysql, you will just need to be in the terminal. Use the following command to export the db to the directory you are currently in.
Best practice states that the /home/user/.my.cnf or /root/.my.cnf file should be created (depending on what user you are taking the dump with) with the appropriate credentials before taking a mysql dump. This is not mandatory but certainly makes life easier when working with mysql

You can view your mysql databases without logging into mysql with the following command:

mysql -e "show databases"

mysqlshow