3 2 * * * ~/db.sh 2>&1 >> ~/_backup/db.log
Note that the order of redirection is important: in this crontab entry the standard error is redirected to the standard output, when the standard output still points to the terminal. In this way the standard error is not redirected to the file db.log. At this point you can check the root's mail to see if cron has sent any standard error via mail to the crontab's owner (default behavior).
Then just reverse the two redirections in order to have both stdout and stderr sent to the log file:
3 2 * * * ~/db.sh >> ~/_backup/db.log 2>&1