Galyn Wiemers explains the "obedience of faith" by teaching Romans 1:5. If a person obeys the gospel it means they accept Jesus Christ as Lord. This submission is obedience. This places
you in the kingdom of God and the family of the saved. It is logical and common sense that from that point on you will pursue an obedient lifestyle before the king. If a person disobeys God after salvation they have still been obedient but are not living out what is in their hearts. They are living contrary to the convictions that are in them, the Holy Spirit and in the Word.
The notes are here - http://generationword.com/notes/romans/03-Romans_1_1-7.pdf