This is a tricky one, I have the following output:
mysqldump: Got error: 1045: Access denied for user \'root\'@\'localhost\' (using password: YES) when tr
If you're able to connect to the database using mysql, but you get an error for mysqldump, then the problem may be that you lack privileges to lock the table.
Try the --single-transaction option in that case.
mysqldump -h database.example.com -u mydbuser -p mydatabase --single-transaction > /home/mylinuxuser/mydatabase.sql