Today we will look at the form वायव्यस्य nGs from श्रीमद्भागवतम् Sb10.63.13.

ब्रह्मास्त्रस्य च ब्रह्मास्त्रं वायव्यस्य च पार्वतम् ।
आग्नेयस्य च पार्जन्यं नैजं पाशुपतस्य च ∥१०-६३-१३∥

श्रीधर-स्वामि-टीका
प्रत्यस्त्राण्येवाह – ब्रह्मास्त्रस्येति । नैजं नारायणास्त्रम् ∥१३∥

Gita Press translation – “Against Brahmāstra He employed Brahmāstra; against Vāyavyāstra He employed the Pārvatāstra; against the fiery missile He employed the Pārjanyāstra and against the Pāśupatāstra He employed His own Nārāyaṇāstra (13).

The above verse has previously appeared in the following post – पाशुपतस्य nGs

वायुर्देवतास्‍येति = वायव्यम् (अस्त्रम्) – (a missile) of which Vāyu is the presiding deity.
In the verses the विवक्षा is षष्ठी-एकवचनम्। Hence the form is वायव्यस्य।

(1) वायु सुँ + यत् । By 4-2-31 वाय्वृतुपित्रुषसो यत्‌ – To denote something of the deity ‘वायु’ or ‘ऋतु’ or ‘पितृ’ or ‘उषस्’, the तद्धित: affix ‘यत्’ may be optionally applied following a syntactically related पदम् in which the सन्धिः operations have been performed, provided the पदम् ends in a nominative case affix and has a base denoting the name of that presiding deity.

Note: The affix ‘यत्’ prescribed by the सूत्रम् 4-2-31 वाय्वृतुपित्रुषसो यत्‌ is अपवादः to the affix ‘अण्’ which would have applied (as per the सूत्रम् 4-2-24 सास्य देवता)।

(2) वायु सुँ + य । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-9 तस्य लोपः।

Note: ‘वायु सुँ + य’ gets the designation प्रातिपदिकम्‌ by 1-2-46 कृत्तद्धितसमासाश्च। This allows 2-4-71 सुपो धातुप्रातिपदिकयोः to apply in the next step.

(3) वायु + य । By 2-4-71 सुपो धातुप्रातिपदिकयोः – A सुँप् affix takes a लुक् elision when it is a part of a धातुः or a प्रातिपदिकम्।

Note: The अङ्गम् ‘वायु’ gets the भ-सञ्ज्ञा by 1-4-18 यचि भम् which allows 6-4-146 ओर्गुणः to apply in the next step.

(4) वायो + य । By 6-4-146 ओर्गुणः – When followed by a तद्धितः affix, the ending letter ‘उ’/’ऊ’ of a अङ्गम् which has the भ-सञ्ज्ञा (ref. 1-4-18 यचि भम्) takes the गुण: substitution (‘ओ’)।

(5) वायव् + य । By 6-1-79 वान्तो यि प्रत्यये – When followed by an affix which begins with the letter ‘य्’, the letters ‘ओ’ and ‘औ’ are replaced by ‘अव्’ and ‘आव्’ respectively.

= वायव्य । Note: The प्रातिपदिकम् ‘वायव्य’ is an adjective. In the present example, it is qualifying the neuter noun अस्त्रम्। Hence, it declines like वन-शब्दः।

Similarly, we can derive the following –
१) ऋतुर्देवतास्‍येति = ऋतव्यम् (हविः) – (an oblation) of which Ṛtu is the presiding deity.