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I'm editing a paper and the sentence I need to fix is, "Thus, the word and its_________ appear seven times in the chapter."

The word in question is a Hebrew word meaning to "rejoice" but the noun form, with an almost identical root meaning "gladness," is part of the seven occurrences. I thought of using "cognate" but that seems to be emphasizing a word "descended from the same language" which is not the emphasis here. I need a word that describes the relationship between a verb and its noun form, e.g., "to fly" and "flight."

Derivative:

(specialized language) a form of something, such as a word, made or developed from another form:

• "Detestable" is a derivative of "detest”.

(Cambridge Dictionary)

A cognate accusative/object is a figure of speech in which the verb and object are etymologically related:

He slept a troubled sleep.
Dance a dance.
Die a peaceful death.

So there shouldn't be any problem writing:

verb x and its cognate noun

Since you're dealing with a language based on consonantal roots, “noun [derived] from the same root” would also work.

The problem with derivation alone is that it assumes that, say, the verb is historically prior to the noun, which may or may not have been the case.

You could use: nominal form, nounal form or, as you yourself suggest, noun form.

Merriam-Webster give the following definitions:

nominal adjective ...

of, relating to, or being a noun or a word or expression taking a noun construction

---

nounal adjective ...

of, relating to, or of the
nature, function, or quality of a noun

And noun can itself be used adjectivally, as it is in the terms noun phrase or noun class.

A cursory glace through Google Books search results suggests nominal form gets extensive use in linguistics texts:

Early Indo-European languages present a wide range of nominal constructions that convey verbal action and combine a noun and a nominal form of the verb...

Archaic Syntax in Indo-European: The Spread of Transitivity in Latin, Brigitte Bauer (2011)

Nounal form seems to be seen more in non-linguistics texts, though it is also used in linguistics too.

Noun form seems to get the most general use, and is also used in linguistics as well.

According to Google Ngram viewer, noun form also seems to be the most common of the three:

For what it's worth, to my mind, noun form is also the nicest - it's simple and straightforward. It's also exactly the words that came to your own mind when trying to find a term!

Absent a more specific term for Semitic languages in general or Hebrew in particular (ask on Linguistics, perhaps, if that's what you want), I'd go for noun form.

I'd also use verb rather than word, so your sentence would read:

Thus, the verb and its noun form appear seven times in the chapter.