Derived verbs, as opposed to basic verbs, are those formed by adding some kind of verbal suffix to another word or root. The root may be verbal or non-verbal. Strictly speaking, the derived verbs are not themselves a distinct verb class, but are rather a collection of similar and related verbal classes. Nevertheless it is useful to have a term for grouping grammatical features common to these verbs classes. The major types of derived verbs are the causatives, formatives and non-verbal derived verbs.
Causatives: The causatives are the result of adding the causative suffixes -tā or -yā to another stem, verbal or otherwise: tul- “to come” vs. tulta- “to send for, fetch, summon, (lit.) cause to come”. Of the two suffixes, -tā is the more common. The resulting verbs are transitive (taking objects).
Formatives: The formatives are the result of adding the suffixes -t(ă) or -y(ă) to a stem, and they are most commonly used with roots which for some reason cannot be used as verbs by themselves: orya- “rise” from the root √OR “up(wards)”. The suffix -y(ă) is more common, to better differentiate the causatives and the formatives. The resulting verbs are often intransitive (unable to take objects).
Non-Verbal Derived: The non-verbal derived verbs are the result of adding a verb suffix to a noun or adjective to turn it into a verb, such as: ninque “white” → ninquita- “to whiten”. The -tā̆, -yā̆ suffixes could be used, but other suffixes were possible, such as -na. In theory nouns or adjectives could be converted directly to verbs if their forms are suitable, that is if they ended in the vowel -a.
The causative verbs had an especially straightforward set of conjugations, and these conjugations tended to expand into other verb classes, especially the non-verbal derived verbs. These are referred to as the “weak” conjugations. The formatives had more irregularities in their conjugations, especially in their past tenses, and Tolkien called them the “half-strong” verbs as a result.
Neo-Quenya: Some Neo-Quenya writers (including myself at times) use the term “derived verbs” as a synonym for “weak verbs”, since the weak conjugations are very common among derived verbs. This is an oversimplification, but not too far from the truth. Another common Neo-Quenya term for this group is “a-stem verbs” since their verb stems end in a, but I avoid this term myself because it is too closed to the more specific a-verb class as identified by Tolkien.