"因轻信而产生的" can be translated as "arising from or resulting from credulity" or "stemming from blind trust". Here are some example sentences for context:
1、 The mistakes he made were arising from/resulting from his credulity.
（他犯的错误是因轻信而产生的。）
2、 The problems encountered in this project stemmed from the team's blind trust in unreliable data.
（这个项目中遇到的问题是因团队轻信不可靠的数据而产生的。）