Text 9

janma karma ca me divyam
evam yo vetti tattvatah
tyaktva deham punar janma
naiti mam eti so ’rjuna

Translation

One who knows the transcendental nature of My appearance and activities does not, upon leaving the body, take his birth again in this material world, but attains My eternal abode, O Arjuna. 

Commentary by Srila Prabhupada 

The Lord’s descent from His transcendental abode is already explained in the 6th verse. One who can understand the truth of the appearance of the Personality of Godhead is already liberated from material bondage, and therefore he returns to the kingdom of God immediately after quitting this present material body. Such liberation of the living entity from material bondage is not at all easy. The impersonalists and the yogis attain liberation only after much trouble and many, many births. Even then, the liberation they achieve—merging into the impersonal brahmajyoti of the Lord—is only partial, and there is the risk of returning to this material world. But the devotee, simply by understanding the transcendental nature of the body and activities of the Lord, attains the abode of the Lord after ending this body and does not run the risk of returning to this material world. In the Brahma-samhita (5.33) it is stated that the Lord has many, many forms and incarnations: advaitam acyutam anadim ananta-rupam. Although there are many transcendental forms of the Lord, they are still one and the same Supreme Personality of Godhead. One has to understand this fact with conviction, although it is incomprehensible to mundane scholars and empiric philosophers. As stated in the Vedas (Purusha-bodhini Upanishad): 

eko devo nitya-lilanurakto
bhakta-vyapi hrdy antar-atma 

“The one Supreme Personality of Godhead is eternally engaged in many, many transcendental forms in relationships with His unalloyed devotees.” This Vedic version is confirmed in this verse of the Gita personally by the Lord. He who accepts this truth on the strength of the authority of the Vedas and of the Supreme Personality of Godhead and who does not waste time in philosophical speculations attains the highest perfectional stage of liberation. Simply by accepting this truth on faith, one can, without a doubt, attain liberation. The Vedic version tat tvam asi is actually applied in this case. Anyone who understands Lord Krishna to be the Supreme, or who says unto the Lord “You are the same Supreme Brahman, the Personality of Godhead,” is certainly liberated instantly, and consequently his entrance into the transcendental association of the Lord is guaranteed. In other words, such a faithful devotee of the Lord attains perfection, and this is confirmed by the following Vedic assertion: 

tam eva viditvati mrityum eti
nanyah pantha vidyate ’yanaya 

“One can attain the perfect stage of liberation from birth and death simply by knowing the Lord, the Supreme Personality of Godhead, and there is no other way to achieve this perfection.” (Shvetasvatara Upanishad 3.8) That there is no alternative means that anyone who does not understand Lord Krishna as the Supreme Personality of Godhead is surely in the mode of ignorance and consequently he will not attain salvation simply, so to speak, by licking the outer surface of the bottle of honey, or by interpreting the Bhagavad-gita according to mundane scholarship. Such empiric philosophers may assume very important roles in the material world, but they are not necessarily eligible for liberation. Such puffed-up mundane scholars have to wait for the causeless mercy of the devotee of the Lord. One should therefore cultivate Krishna consciousness with faith and knowledge, and in this way attain perfection.

Commentary by Sri Visvanatha Cakravarti Thakur

You will be successful just by knowing in truth about my birth which was previously described, and after my birth, my activities. That is expressed in this verse.

Ramanujacarya and Madhusudana SarasvatI say that divya means "non material, spiritual." Sridhara Svami says divya means "uncommon." As this means that it is not related to this material world, it also means "spiritual." Being spiritual, beyond the gunas, means that the Lord's birth and activities are eternal. Jiva Gosvami also explains, quoting from Bhagavatam in the Bhagavat Sandarbha that the Lord has no birth or activities:

na vidyate yasya ca janma karma va
na nama-rupe guna-dosa eva va
tathapi lokapyaya-sambhavaya yah
sva-mayaya tany anukalam rcchati

The Supreme Personality of Godhead has no material birth, activities, name, form, qualities or faults. To fulfill the purpose for which this material world is created and destroyed, He comes in the form of a human being like Lord Rama or Lord Krishna by His original internal potency. He has immense potency, and in various forms, all free from material contamination, He acts wonderfully. He is therefore the Supreme Brahman. I offer my respects to Him. SB 8.3.8

Or the word divya can mean not approachable by logic, or inconceivable, on the strength of the words of sruti and smrti. The Purusa Bodhini Sruti (4.3) of the Pippaladi branch of the Vedas says:

eko devo nitya-lilanurakto bhakta-vyapi bhakta-hrdayantaratma

This one, who is inconceivable (deva), engaged in eternal pastimes, is spread in the devotees and resides in the devotee's heart. The eternal nature of the Lord's birth and activities is mentioned frequently in the Bhagavatam as well.

Yo vetti tattvatah means "he who knows my birth and activitie are truly eternal," based on my statements that I am unborn anc with indestructible body (ajo 'pi san avyayatma) and that my birth and activities are non material (janma karma ca me divyam), and not just an appearance of being eternal, dependent on some sort of trick.

Yo vetti tattvatah can also mean "one who knows me as the ver form of Brahman."   This is because later Krishna will say: om tat sad iti nirdeso brahmanas trividhah smrtah: the three words om tat sat all indicate brahman. (Gita 17.18) Therefore tattva means the state of being brahman (tat). Yo vetti tattvatah means "one who know me as the form of brahman."

That person does not take birth again, but rather attains me. The words tyaktva deham only indicate the last condition, for, not only on giving up the body one does not take birth again, but even not giving up the body, before that, one attains me.           

Ramanujacarya says, "Destroying all sins which are unfavorable for surrender to me by true knowledge of my spiritual birth and activities, taking shelter of me in this life in the prescribed way, that person who holds me alone as dear, constantly thinking of me, attains me."