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Śrīmad-Bhāgavatam 7.2.9

తస్మిన్ కూటేఽహితే నష్టే కృత్తమూలే వనస్పతౌ । విటపా ఇవ శుష్యన్తి విష్ణుప్రాణా దివౌకస: ॥ ౯ ॥
tasmin kūṭe ’hite naṣṭe
[tasmin koote ’hite nashte]
kṛtta-mūle vanas-patau
[kritta-moole vanas-patau]
viṭapā iva śuṣyanti
[vitapaa iva shushyanti]
viṣṇu-prāṇā divaukasaḥ
[vishnu-praanaa divaukasah]
Word-for-word
tasmin — when He kūṭe — the most deceitful ahite — enemy naṣṭe — is finished kṛtta-mūle — having its roots cut off vanas-patau — a tree viṭapāḥ — the branches and leaves iva — like śuṣyanti — dry up viṣṇu-prāṇāḥ — whose life is Lord Viṣṇu diva-okasaḥ — the demigods.
Blended reading (Sanskrit + English inline)
tasmin kūṭe ’hite naṣṭe
tasmin
when He
kūṭe
the most deceitful
kṛtta-mūle vanas-patau
viṭapā iva śuṣyanti
viṣṇu-prāṇā divaukasaḥ
ahite
enemy
naṣṭe
is finished
kṛtta-mūle
having its roots cut off
vanas-patau
a tree
viṭapāḥ
the branches and leaves
iva
like
śuṣyanti
dry up
viṣṇu-prāṇāḥ
whose life is Lord Viṣṇu
diva-okasaḥ
the demigods.
When the root of a tree is cut and the tree falls down, its branches and twigs automatically dry up. Similarly, when I have killed this diplomatic Viṣṇu, the demigods, for whom Lord Viṣṇu is the life and soul, will lose the source of their life and wither away.
Purport

The difference between the demigods and the demons is here explained. The demigods always follow the instructions of the Supreme Personality of Godhead, whereas the demons simply plan to disturb or kill Him. Nevertheless, sometimes the demons very much appreciate the full dependence of the demigods upon the mercy of the Lord. This is indirect glorification of the demigods by the demons.

— A.C. Bhaktivedanta Swami Prabhupāda
Gauḍīya Ācāryas
Viśvanātha Cakravartī Ṭhākura Gauḍīya
Translation
The devatās, whose life is Viṣṇu, will wither away when cheating Viṣṇu is dead, just as branches wither away when the root is cut. Kūṭe ahite means “Viṣṇu having deceptive actions.” But it also means “Viṣṇu who fights against cheaters like me.” Thus this is my good fortune. There is also good fortune for the devatās. They live only for Viṣṇu. Nāsṭe can also mean that Viṣṇu becomes invisible, since he cannot be destroyed. When he disappears from their sight, just as a tree dries up when the root is cut, so the devatās, whose life is Viṣṇu, will dry up, out of separation. The devatās are fortunate, having Viṣṇu as their very life.
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