The unique phrase "fruits of righteousness" has many supporting teachings, the most famous of which is where the Lord Jesus compares Himself to a "vine" and we who are His adopted sons and daughters to "branches" (John 15:1-6).
Paul reminded the Philippian church that the fruits ultimately result from Jesus Christ, just as Jesus illustrated. We "cannot bear fruit" by ourselves (John 15:4). Not only does our very life come from God, but the ability to produce godly fruit can only come through and by God.
Isaiah noted that all of our self-produced righteous deeds are like "filthy rags" (Isaiah 64:6). The fruit for which we are "ordained" (John 15:16) has its source in the thrice-holy Godhead and its manifestation by the fruit of the Holy Spirit in our lives (Galatians 5:22-23).
Those Holy Spirit character traits are the innate property of the vine that becomes instilled in the branches, or us. This enables us to bring forth the fruit that represents the "DNA" of the vine in which we are abiding. Being connected to the vine makes it possible for us to "walk worthy of the Lord unto all pleasing, being fruitful in every good work, and increasing in the knowledge of God" (Colossians 1:10).
The "husbandman" (God the Father) is superintending the vineyard (John 15:1). When branches wither and do not produce fruit (see also Matthew 13:18-23), they are taken away. The branches that do produce are purged (Greek kathairo, "cleaned up"). As Peter noted, "his divine power hath given unto us all things that pertain unto life and godliness" (2 Peter 1:3). With God, "all things are possible" (Matthew 19:26). Without Him, "|we| can do nothing" (John 15:5). HMM III http://www.icr.org/article/5957/