Repentance From Dead Works
As Christians everyday we are told to repent from sin but this sin is just the fruit, dead works are the root so these dead works in essence results in sin.
Dead works are not sins but they are what lead us to sin, dead works are the so-called good works people to that make them believe they are right with God i.e they think they are righteous because of their doings. Only God can make us righteous, our actions can't and people tend not to understand this. It is true that when you are righteous you will always do good works but if you want to take it the other way round by doing acclaimed good works to make yourself righteous then you will miss it.
Hebrew 6:1
Therefore let us move beyond the elementary teachings about Christ and be taken forward to maturity, not laying again the foundation of repentance from acts that lead to death, and of faith in God
If for instance you go about preaching the gospel believing that the action you are performing will make you righteous then you are going about it the wrong way and that is a dead work. In another scenario if you preach the gospel to people because you believe already that you are righteous and you just want to share the good news of the One that made you righteous to people so they too can come out of sin then you have indeed been dwelling in the righteousness of christ Jesus.
Our self works cannot make us whole, Jesus has died on the cross to make us whole again and when we believe that and begin to live by that understanding we'll become righteous.