I think you can do that from inside directadmin.
with my theme im using there is a little figure in the top right corner,
(has like messages, login keys, login history, password)
click password and you should see "Current DirectAdmin Password:"
and "Enter new password:"
then 3 check boxes under where you enter the passwords,
DirectAdmin Account, Main FTP Account and Main Database Account.
i would advise making sure they are all checked though,
so they share the same master password.
"Can I change the password of MySQL database independently"
i assume you could do that but i would not advise it.
by only checking "Main Database Account"
the location of this option may depend on the theme you
are using for your directadmin.