Is it possible to derive a custom boolean function from a truth table in terms of known boolean operators?
Yes. This could be done by inspection, or by Karnaugh maps. Although there are different methods.

The most basic method is to express the output obtained from the truth table, as a sum of products or products of sums, following the rules of Boolean algebra.
Thus, the canonical expression function described by the truth table is achieved.
By Karnaugh map, you can reduce that logic function.