Derivative can be anything for liberi.
closed as unclear what you're asking by Cerberus♦ Jan 16 at 0:46
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If you are actually looking for words derived from lībĕr, or lībĕri, ōrum, then I suggest you look up all the words beginning with lib- in your own language, if that is English, French, Spanish.
If you want words from which lībĕri, ōrum, is derived, this may help. It is taken from the Perseus Charlton T. Lewis; Charles Short Latin Dictionary
līber, ĕra, ĕrum old form, loebesum et loebertatem antiqui dicebant liberum et libertatem. Ita Graeci λοιβὴν et λείβειν, Paul. ex Fest. p. 121 Müll.; cf. 2. Liber), adj. Gr. root λιφ-, λίπτω, to desire; cf. Sanscr. lub-dhas, desirous; Lat. libet, libido,
In Latin children are only lībĕri if they are
"A Free, in a social point of view, not a slave or
B Free, in a political point of view; said both of a people not under monarchical rule and of one not in subjection to another people"
Otherwise children are puer or juvenis (from the 15th year); but the same person is often called in one place adulescens, and in another juvenis.