Something interesting that I came across last week in studying: John 3:36 is a commonly quoted scripture. The KJV, NKJV, and Youngs roughly say: "He who believes (pisteuo) in the Son has everlasting life; and he who does not believe (apeitheo) the Son shall not see life, but the wrath of God abides on him."
Other versions, such ASV, NASV, ESV, RSV, etc., say, "He who believes in the Son has everlasting life; and he who does not obey the Son shall not see life, but the wrath of God abides on him.”
The same thing exists in Hebrews 3:18-19, "And to whom did He swear that they would not enter His rest, but to those who did not obey? So we see that they could not enter in because of unbelief."
How do the writers get “obey?” It makes sense, as if you do believe, you will obey. But obey is a definition far down the list in the concordance.
The Greek word apeitheo is a compound word. The prefix a means "not" and the verb peitho means "to obey" when used in the active sense or "to be persuaded" when used in the passive sense. In John 3:36 the verb is in the active present tense, so "disobey" would be the correct literal translation.
Jesus' contrast of believe (pisteuo) against disobey (apeitheo) demonstrates that God sees belief and obedience to be two sides of the same coin. So many denominational teachers have claimed that faith and works are separate issues and that we are saved by faith alone that people are often surprised to find that God sees things differently. James said, "You see then that a man is justified by works, and not by faith only" (James 2:24). Belief cannot be separated from obedience. A person who is obeying is demonstrating his belief. A person who believes won't sit there and do nothing.
The writer of Hebrews makes the same parallel. Hebrews 3:18-19 shows that disobedience and disbelief are two views of the same problem.
Thus, in Acts 14:2 it says, "But the unbelieving Jews stirred up the Gentiles and poisoned their minds against the brethren." But it literally says the "disobeying Jews;" the Jews were actively showing their disbelief by stirring up the Gentiles against the Gospel -- an act of disobedience.
"Unbelief" is not a wrong translation for apeitheo but it does lose a bit of the richness that is present in the text.
Thanks for answering my question!