SQLite Forum

Error Code : Error while executing SQL query on database ‘test’: no such column: price
This will probably calculate the number of days: (julianday(date_out) - julianday(date_back) + 1)

You need to use
to restrict changes to the affected row. 

 WHERE rental_cost IS NULL
will update ALL of the rows that have a NULL rental cost

The price in the subselect will be the one from the first Rental record visited in the subselect. I don't think that is what you intend. If you want the price from the affected row, just use NEW.price instead.