After hours and hours work, I created a solution like the below. I copy paste for other people that can benefit.
First create a script file and give this file executable permission.
# cd /etc/cron.daily/
# touch /etc/cron.daily/dbbackup-daily.sh
# chmod 755 /etc/cron.daily/dbbackup-daily.sh
# vi /etc/cron.daily/dbbackup-daily.sh
Then copy following lines into file with Shift+Ins
#!/bin/sh
now="$(date +'%d_%m_%Y_%H_%M_%S')"
filename="db_backup_$now".gz
backupfolder="/var/www/vhosts/example.com/httpdocs/backups"
fullpathbackupfile="$backupfolder/$filename"
logfile="$backupfolder/"backup_log_"$(date +'%Y_%m')".txt
echo "mysqldump started at $(date +'%d-%m-%Y %H:%M:%S')" >> "$logfile"
mysqldump --user=mydbuser --password=mypass --default-character-set=utf8 mydatabase | gzip > "$fullpathbackupfile"
echo "mysqldump finished at $(date +'%d-%m-%Y %H:%M:%S')" >> "$logfile"
chown myuser "$fullpathbackupfile"
chown myuser "$logfile"
echo "file permission changed" >> "$logfile"
find "$backupfolder" -name db_backup_* -mtime +8 -exec rm {} \;
echo "old files deleted" >> "$logfile"
echo "operation finished at $(date +'%d-%m-%Y %H:%M:%S')" >> "$logfile"
echo "*****************" >> "$logfile"
exit 0
Edit:
If you use InnoDB and backup takes too much time, you can add "single-transaction" argument to prevent locking. So mysqldump line will be like this:
mysqldump --user=mydbuser --password=mypass --default-character-set=utf8
--single-transaction mydatabase | gzip > "$fullpathbackupfile"