Today we will look at the form पाशुपतस्य 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).

पशुपतिर्देवतास्‍येति = पाशुपतम् (अस्त्रम्) – (a missile) of which Lord Śiva is the presiding deity.
In the verses the विवक्षा is षष्ठी-एकवचनम्। Hence the form is पाशुपतस्य।

(1) पशुपति सुँ + अण् । By 4-2-24 सास्य देवता – To denote something of a particular deity, the तद्धित: affix ‘अण्’ (prescribed by 4-1-83 प्राग्दीव्यतोऽण्) 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: Since the base ‘पशुपति’ is a compound with ‘पति’ as its final member, the affix ‘ण्य’ (prescribed by the सूत्रम् 4-1-85 दित्यदित्यादित्यपत्युत्तरपदाण्ण्यः) overrules the default affix ‘अण्’ (prescribed by the सूत्रम् 4-1-83 प्राग्दीव्यतोऽण्)। But since ‘पशुपति’ is specifically listed in the अश्वपत्यादि-गण:, the affix ‘ण्य’ is in turn overruled by the affix ‘अण्’ prescribed by the सूत्रम् 4-1-84 अश्वपत्यादिभ्यश्च – The तद्धित: affix ‘अण्’ is authorized for all rules from here (4-1-84) down prior to the सूत्रम् 4-4-2 तेन दीव्यति खनति जयति जितम्, provided it is applied to a पदम् which has ‘अश्वपति’ etc (listed in the अश्वपत्यादि-गण:) as its base.

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

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

(3) पशुपति + अ । 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 affix ‘अण्’ is a णित् (has the letter ‘ण्’ as इत्)। This allows 7-2-117 तद्धितेष्वचामादेः to apply in the next step.

(4) पाशुपति + अ । By 7-2-117 तद्धितेष्वचामादेः – The first vowel among the vowels of a अङ्गम् which is followed by a तद्धित: affix (ref. 4-1-76 तद्धिताः) which is either a ञित् (has the letter ‘ञ्’ as a इत्) or a णित् (has the letter ‘ण्’ as a इत्) takes the वृद्धि: (ref. 1-1-1 वृद्धिरादैच्) substitute.

Note: The अङ्गम् ‘पाशुपति’ gets the भ-सञ्ज्ञा by 1-4-18 यचि भम् which allows 6-4-148 यस्येति च to apply in the next step.

(5) पाशुपत् + अ । By 6-4-148 यस्येति च – When the letter ‘ई’ or a ‘तद्धित’ affix follows, the (ending) इ-वर्ण: (letter ‘इ’ or ‘ई’) or the (ending) अवर्ण: (letter ‘अ’ or ‘आ’) of the अङ्गम् with the भ-सञ्ज्ञा takes elision (लोपः)।

= पाशुपत । Note: The प्रातिपदिकम् ‘पाशुपत’ 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) गणपतिर्देवतास्‍येति = गाणपतः (मन्त्रः) – (a mantra) of which Lord Gaṇeśa is the presiding deity.