Tools/Methods to investigate slow query

I have a query with a subquery, both are fast but when combined they take forever (meaning whatever time above what is acceptable in my application). I tried using 'explain' to see what's going on, it didn't help me much. What other ways are there to investigate slow queries? Below are the specific details of my problem. I have a list of products, I want to find the date of the first vendor event for each product. If I get the list of event IDs, the query goes fast (each product might have multiple events, they are created in chronological order so min event ID is the earliest; ProdID is indexed); then I use this list of event IDs to get the date, this second query goes fast too (event ID is the primary key, therefore indexed). But if I use the first query as a subquery of the second, it takes forever. Query 1: mysql> select min(VendorEventID) from Vendor_Events where ProdID in (598446938, 598446984, 598447024, 598447054, 598447311, 598447523, 598447764, 598447778, 598448000, 598448048) and vendorid = 12 group by ProdID ; +--------------------+ | min(VendorEventID) | +--------------------+ | 11217790121 | | 11217792453 | | 11217793912 | | 11217793894 | | 11217794825 | | 11217815018 | | 11217813148 | | 11217828936 | | 11217830215 | | 11217829202 | +--------------------+ 10 rows in set (0.00 sec) Query 2: mysql> select * from Vendor_Events where VendorEventID in ( 11217790121, 11217792453, 11217793912, 11217793894, 11217794825, 11217815018, 11217813148, 11217828936, 11217830215, 11217829202 ) ; +---------------+----------+-----------+---------------------+------------+--------+ | VendorEventID | VendorID | ProdID | LoggedDate | VendorType | NameID | +---------------+----------+-----------+---------------------+------------+--------+ | 11217790121 | 12 | 598446938 | 2016-12-07 16:33:58 | 2 | 32 | | 11217792453 | 12 | 598446984 | 2016-12-07 16:34:14 | 2 | 32 | | 11217793894 | 12 | 598447054 | 2016-12-07 16:34:29 | 2 | 32 | | 11217793912 | 12 | 598447024 | 2016-12-07 16:34:29 | 2 | 32 | | 11217794825 | 12 | 598447311 | 2016-12-07 16:34:33 | 2 | 32 | | 11217813148 | 12 | 598447764 | 2016-12-07 16:37:10 | 2 | 32 | | 11217815018 | 12 | 598447523 | 2016-12-07 16:37:24 | 2 | 32 | | 11217828936 | 12 | 598447778 | 2016-12-07 16:39:54 | 2 | 32 | | 11217829202 | 12 | 598448048 | 2016-12-07 16:39:55 | 2 | 32 | | 11217830215 | 12 | 598448000 | 2016-12-07 16:40:04 | 2 | 32 | +---------------+----------+-----------+---------------------+------------+--------+ 10 rows in set (0.04 sec) Explain them combined: mysql> explain select * from Vendor_Events where VendorEventID in ( select min(VendorEventID) from Vendor_Events where ProdID in (598446938, 598446984, 598447024, 598447054, 598447311, 598447523, 598447764, 598447778, 598448000, 598448048) and vendorid = 12 group by ProdID ) ; +----+--------------------+---------------+-------+-----------------+----------+---------+------+----------+--------------------------+ | id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra | +----+--------------------+---------------+-------+-----------------+----------+---------+------+----------+--------------------------+ | 1 | PRIMARY | Vendor_Events | ALL | NULL | NULL | NULL | NULL | 78536406 | Using where | | 2 | DEPENDENT SUBQUERY | Vendor_Events | range | ProdID,ProdID_2 | ProdID_2 | 16 | NULL | 15 | Using where; Using index | +----+--------------------+---------------+-------+-----------------+----------+---------+------+----------+--------------------------+ 2 rows in set (0.00 sec) Of course if anyone can help me figure out what's causing the query to be super slow, I'd appreciate. But if people want to tell me what other ways are there to investigate slow queries, I'd like that too, since we all face slow queries every now and then. ;-)