B.G 15.16, 17 and 18

द्वाविमौ पुरुषौ लोके क्षरश्चाक्षर एव च। क्षरः सर्वाणि भूतानि कूटस्थोऽक्षर उच्यते ॥१६॥

dvāv imau puruṣau loke kṣaraś cākṣara eva ca। kṣaraḥ sarvāṇi bhūtāni kūṭastho'kṣara ucyate ॥16॥

[द्वौ (dvau) - two; इमौ (imau) - these; पुरुषौ (puruṣau) - beings; लोके (loke) - in the world; क्षरः (kṣaraḥ) - perishable; च (ca) - and; अक्षरः (akṣaraḥ) - imperishable; एव (eva) - indeed; च (ca) - and; क्षरः (kṣaraḥ) - perishable; सर्वाणि (sarvāṇi) - all; भूतानि (bhūtāni) - beings; कूटस्थः (kūṭasthaḥ) - the insentient Prakrti; अक्षरः (akṣaraḥ) - imperishable; उच्यते (ucyate) - is called;]

In this world, there are two types of beings: Kṣara i.e. the changing and Akṣaraḥ i.e. the unchanging. All creatures are Kṣaras i.e. the changing, but the imperishable insentient, i.e. Prakrti, is called the Akṣaraḥ i.e. the unchanging.

उत्तमः पुरुषस्त्वन्यः परमात्मेत्युदाहृतः। यो लोकत्रयमाविश्य बिभर्त्यव्यय ईश्वरः ॥१७॥

uttamaḥ puruṣastvanyaḥ paramātmetyudāhṛtaḥ। yo lokatrayamāviśya bibhartyavyaya īśvaraḥ ॥17॥

[उत्तमः (uttamaḥ) - the highest; पुरुषः (puruṣaḥ) - person; तु (tu) - but; अन्यः (anyaḥ) - another; परमात्मा (paramātmā) - the Supreme Ātman ; इति (iti) - thus; उदाहृतः (udāhṛtaḥ) - is said; यः (yaḥ) - who; लोकत्रयम् (lokatrayam) - the three worlds; आविश्य (āviśya) - entering; बिभर्ति (bibharti) - sustains; अव्ययः (avyayaḥ) - imperishable Prakrti; ईश्वरः (īśvaraḥ) - the Lord;]

The highest person is said to be another, the Supreme Ātman, who, entering the three worlds, sustains, the Lord of the imperishable Paakrti.

यस्मात् क्षरमतीतोऽहमक्षरादपि चोत्तमः। अतोऽस्मि लोके वेदे च प्रथितः पुरुषोत्तमः ॥१८॥

yasmāt kṣaramatīto'hamakṣarādapi cottamaḥ। ato'smi loke vede ca prathitaḥ puruṣottamaḥ ॥18॥

[यस्मात् (yasmāt) - because; क्षरम् (kṣaram) - subjected to change; अतीतः (atītaḥ) - transcend; अहम् (aham) - I; अक्षरात् (akṣarāt) - imperishable; अपि (api) - also; च (ca) - and; उत्तमः (uttamaḥ) - supreme; अतः (ataḥ) - therefore; अस्मि (asmi) - am; लोके (loke) - in the world; वेदे (vede) - in the Vedas; च (ca) - and; प्रथितः (prathitaḥ) - celebrated; पुरुषोत्तमः (puruṣottamaḥ) - as the Supreme Person;]

I am known as the Supreme Person in the world and the Vedas because I transcend both the 'Kshara', subjected to change, and the 'Akshara', the unchanging.

Gīta Tātparya 15.16, 17, and 18

He is known as 'Purushottama', the Supreme Being, because he transcends both the 'Kshara' the changing, and 'Akshara' the unchanging.

ब्रह्मरुद्रादयः सर्वे शरीरक्षरणात् क्षराः। श्रीरक्षरात्मेत्युदिता नित्यचिद्देहका यतः। चेतनाचेतनस्यास्य राशेः संस्थापकत्वतः। कूटस्थ आत्मा सा ज्ञेया परमात्मा हरिः स्वयम्॥

brahmarudrādayaḥ sarve śarīrakṣaraṇāt kṣarāḥ। śrīrakṣarātmetyuditā nityaciddehakā yataḥ। cetanācetanasyāsya rāśeḥ saṃsthāpakatvataḥ। kūṭastha ātmā sā jñeyā paramātmā hariḥ svayam॥

[ब्रह्मरुद्रादयः (brahmarudrādayaḥ) - Brahma, Rudra, and others; सर्वे (sarve) - all; शरीरक्षरणात् (śarīrakṣaraṇāt) - due to the decay of the body; क्षराः (kṣarāḥ) - perishable; श्रीरक्षरात्मा (śrīrakṣarātmā) - the imperishable being; इति (iti) - thus; उदिता (uditā) - is said; नित्यचिद्देहका (nityaciddehakā) - eternal conscious bodies; यतः (yataḥ) - because; चेतनाचेतनस्य (cetanācetanasyasya) - of the sentient and insentient; अस्य (asya) - of this; राशेः (rāśeḥ) - aggregate; संस्थापकत्वतः (saṃsthāpakatvataḥ) - due to being the foundation; कूटस्थ (kūṭastha) - unchanging; आत्मा (ātmā) - ātman; सा (sā) - that; ज्ञेया (jñeyā) - is to be known; परमात्मा (paramātmā) - the Supreme being; हरिः (hariḥ) - Hari; स्वयम् (svayam) - himself;]

Brahma, Rudra, and others are considered perishable because their bodies decay. However, the Ātman, which is eternal and conscious, is imperishable and serves as the foundation for both the sentient and the insentient. This unchanging Ātman is recognized as the Supreme Being, Lord Hari himself.

क्षराक्षरात्मनोः यस्मादुत्तमः स सदाऽनयोः। पुरुषोत्तमनाम्नातः प्रसिद्धो लोकवेदयोः॥

kṣarākṣarātmanoḥ yasmāduttamaḥ sa sadā'nayoḥ। puruṣottamanāmnātaḥ prasiddho lokavedayoḥ॥

[क्षर (kṣara) - perishable; अक्षर (akṣara) - imperishable; आत्मनोः (ātmanoḥ) - of the self; यस्मात् (yasmāt) - because; उत्तमः (uttamaḥ) - supreme; सः (saḥ) - he; सदा (sadā) - always; अनयोः (anayoḥ) - of these two; पुरुषोत्तम (puruṣottama) - as Purushottama; नाम्ना (nāmnā) - by name; आतः (ātaḥ) - known; प्रसिद्धः (prasiddhaḥ) - famous; लोकवेदयोः (lokavedayoḥ) - in the world and the Vedas;]

He is known as 'Purushottama', the Supreme Being, because he transcends both the 'Kshara' the changing, and 'Akshara', the unchanging, and is renowned in both worldly and Vedic contexts.

इति नारायणश्रुतिः ॥

iti nārāyaṇaśrutiḥ ॥

[इति (iti) - thus; नारायण (nārāyaṇa) - Narayana; श्रुतिः (śrutiḥ) - scripture;]

(Thus, the scripture of Narayana.)

- stated thus in the Narayana Vedic text.

॥ इति श्रीमदानन्दतीर्थभगवत्पादाचार्यविरचिते श्रीभगवद्गीतातात्पर्यनिर्णये पञ्चदशोध्यायः ॥

॥ iti śrīmadānandatīrthabhagavatpādācāryaviracite śrībhagavadgītātātparyanirṇaye pañcadaśādhyāyaḥ ॥

[इति (iti) - thus; श्रीमद् (śrīmad) - revered; आनन्दतीर्थ (ānandatīrtha) - Ānandatīrtha; भगवत्पाद (bhagavatpāda) - Bhagavatpāda; आचार्य (ācārya) - teacher; विरचिते (viracite) - composed; श्रीभगवद्गीता (śrībhagavadgītā) - Śrī Bhagavad Gītā; तात्पर्य (tātparya) - interpretation; निर्णये (nirṇaye) - decision; पञ्चदश (pañcadaśa) - fifteenth; अध्यायः (adhyāyaḥ) - chapter;]

Thus ends the fifteenth chapter in the revered teacher Ānandatīrtha Bhagavatpāda's composition, the purport of the Śrī Bhagavad Gītā.