should I select columns before or after join?

I have a join that takes a lot of time:

select t1.*, t.b from t1 join (select id, b from t2) t on t1.id = t.id

I have an index on id in t2.

1. Is index on id preserved when I create a derived table t?
2. In terms of performance, do I need to select from t2, or would this be always as fast:

select t1.*, t.b from t1 join t2 t on t1.id = t.id ?