राजश्वशुराद्यत्

Operational rule vidhi

The affix यत् comes in the sense of the descendant after the words राजन् and श्वसुर.

Word by word (padaccheda)

Left context राज- श्वशुरात् pañcamī · ekavacanaSubstitute / term य prathamā · ekavacana

Left context Pañcamī (5th case): "after X", the operation applies to what follows (1.1.67 तस्मादित्युत्तरस्य). Also used for limits and sources.
Substitute / term Prathamā (1st case): in operational rules, the substitute or the thing introduced; in definitions, the term or its referent.

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Full reading

राज-श्वशुरात् यत्

Pāṇini leaves out words that carry over from earlier sūtras. Expand to see the rule as a reader actually understands it.

Commentary

The affix यत् comes in the sense of the descendant after the words राजन् and श्वसुर।
This debars अण् and अञ् respectively. Thus राजन्यः 4.4.168 'a person of Kshatriya class'. This is the special meaning of the word; it does not mean 'the son of a Raja.' The word राजनः will mean 'the son of a King.' So also श्वशुरर्यः 'son of the father-in-in-law.'

Śrīśa Chandra Vasu, The Ashtadhyayi of Panini (1897), via ashtadhyayi.com.