A derivative citizenship is one that is derived from the citizenship of the someone else, usually the father of the husband. In the United States, foreign born children under the age of majority when their father naturalized would generally be considered naturalized themselves and would not have to go through the process themselves.
If your ancestor immigrated as a child, indicates he is naturalized but you cannot find any naturalization papers in his name, then consider the possibility that he had derivative citizenship through a father’s naturalization.
Genealogy Tip of the Day is proudly sponsored by GenealogyBank. Try their “GenealogyBank Search” and see what discoveries you make.