Prāṇa is the vital air of life, a more subtle element than the ordinary air we can touch. And because prāṇa is so subtle — finer than the tangible manifestations of creation — it is sometimes considered the ultimate source of everything. But even subtle energies such as prāṇa depend for their functional capacity on the supremely subtle Paramātmā. That is the idea Vasudeva expresses here by the word pāratantryāt, “because of dependence.” Just as the velocity of an arrow is derived from the strength of the bowman who shoots it, so all subordinate energies depend on the power of the Supreme Lord.

Furthermore, even when various subtle causes have been empowered with their capacity to act, they cannot act in concert without the Supersoul’s coordinating direction. As Lord Brahmā states in his description of creation in the Second Canto of Śrīmad-Bhāgavatam:

yadaite ’saṅgatā bhāvā
 bhūtendriya-mano-guṇāḥ
yadāyatana-nirmāṇe
 na śekur brahma-vittama

tadā saṁhatya cānyonyaṁ
 bhagavac-chakti-coditāḥ
sad-asattvam upādāya
 cobhayaṁ sasṛjur hy adaḥ

“O Nārada, best of the transcendentalists, the forms of the body cannot manifest as long as these created parts, namely the elements, senses, mind and modes of nature, are not assembled. Thus when all these became assembled by the force of the energy of the Supreme Personality of Godhead, this universe certainly came into being by accepting both the primary and secondary causes of creation.” (Bhāg. 2.5.32-33)