BhG 18.57

syntax

[tvam] (you) mat-paraḥ (for whom I am the supreme) cetasā (with the mind) sarva-karmāṇi (all activities) mayi (in me) sannyasya (after renouncing),
buddhi-yogam (of yoga of intelligence) upāśritya (after taking shelter)
satatam (constantly) mac-cittaḥ (with the mind in me) bhava (you must be).

grammar

cetasā	–	cetas 3n.1 n. – with the mind (from: √cit – to think, cetas – mind, thought, heart, consciousness);
sarva-karmāṇi	–	sarva-karman 2n.3 n.; TP: sarvāṇi karmāṇi iti – all activities (from: sarva – all, whole; √kṛ – to do, karman – activity and its result);
mayi	–	asmat sn. 7n.1 – in me;
saṁnyasya	–	sam-ni-√as (to lay aside, to renounce, to give up) absol. –after renouncing, after giving up;
mat-paraḥ	–	mat-para 1n.1 m. – yasyāhaṁ paro ‘smi saḥ – for whom I am the supreme, devoted to me (from: mat – the basic form of a personal ponoun „I” singular used in compounds; para – beyond, ancient, final, the best, the supreme; suffix: para – devoted, engaged in, mat-para – devoted to me);
buddhi-yogam	–	buddhi-yoga 2n.1 m.; TP: buddhyā kṛtaṁ yogam iti – yoga evolved from intelligence (from: √budh – to wake, to perceive, to understand; buddhi – intelligence, thought, understanding, knowledge, idea, opinion; √yuj – to yoke, to join, to engage, yoga – yoga, yoking, application, a means, one of the schools of Hindu philosophy);
upāśritya	–	upa-ā-√śri (to  adhere, to lean on, to rest on, to depend on) absol. – after taking shelter – of whom? – requires accusative);
mac-cittaḥ	–	mac-citta 1n.1 m. – yasya cittaṁ mayi asti saḥ – whose mind is in me (from: mat – the basic form of a personal ponoun „I” singular used in compounds; √cit – to perceive, to think, PP citta – thought; a thought, mind, heart, consciousness);
satatam	–	av. – constantly (from: sa-tata – constant, uninterrupted);
bhava	–	√bhū (to be) Imperat. P 2v.1 – you must be;

textual variants

mat paraḥ → bhārata (O descendant of Bhārata!);
buddhi-yogam → śuddhi-yogam (yoga of purity);
upāśritya → samāśritya / apāśritya (after taking shelter / after using);

The second pada of verse 18.57 is the same as the second pada of verse BhG 12.6;

Śāṃkara

yasmāt evaṃ—
cetasā vivekabuddhyā sarva-karmāṇi dṛṣṭadṛṣṭarthāni mayi īśvare saṃnyasya yat karoṣi yada nāsīti uktanyāyena, mat-paro’haṃ vāsudevaḥ paro yasya tava sa tvaṃ mat-paraḥ san mayyarpitasarvātmabhāvo buddhi-yogaṃ samāhitabuddhitvaṃ buddhi-yogas taṃ buddhi-yogam apāśrityāpāśrayo’nanyaśaraṇatvaṃ mac-cittaḥ mayy evaś cittaṃ yasya tava sa tvaṃ mac-cittaḥ satataṃ sarvadā bhava

Rāmānuja

yasmād evam, tasmāt
cetasā ātmano madīyatvamanniyāmyatvabuddhyā / uktaṃ hi, „mayi sarvāṇi karmāṇi saṃnyasyādhyātmacetasā” iti / sarvakarmāṇi sakartṛkāṇi sārādhyāni mayi saṃnyasya, matparaḥ aham eva phalatayā prāpya ity anusaṃdhānaḥ, karmāṇi kurvan imam eva buddhiyogam upāśritya satataṃ maccitto bhava

Śrīdhara

yasmād evaṃ tasmāt cetaseti | sarvāṇi karmāṇi | cetasā mayi saṃnyasya samarpya mat-paraḥ aham eva paraḥ prāpyaḥ puruṣārtho yasya sa vyavasāyātmikayā buddhyā yogam upāśritya satataṃ karmānuṣṭhāna-kāle ‚pi brahmārpaṇaṃ brahma-havir iti (Gītā 4.24) nyāyena mayy eva cittaṃ yasya tathābhūto bhava

Viśvanātha

nanu tarhi māṃ prati tvaṃ niścayena kim ājñāpayasi | kim aham ananya-bhakto bhavāmi, kiṃ vānantarokta-lakṣaṇaḥ sakāma-bhakta eva | tatra sarva-prakṛṣṭo ‚nanya-bhakto bhavituṃ na prabhaviṣyasi | nāpi sarva-bhakteṣv apakṛṣṭaḥ sakāma-bhakto bhava | kintu tvaṃ madhyama-bhakto bhavety āha cetaseti | sarva-karmāṇi svāśrama-dharmān vyavahārika-karmāṇi ca mayi sannyasya samarpya, mat-paro ‚ham eva paraḥ prāpyaḥ puruṣārtho yasya sa niṣkāma ity arthaḥ | yad uktaṃ pūrvam eva
yat karoṣi yad aśnāsi
yaj juhoṣi dadāsi yat |
yat tapasyasi kaunteya
tat kuruṣva mad-arpaṇam || iti | (Gītā 9.27)
buddhi-yogaṃ vyavasāyātmikayā buddhyā yogaṃ satataṃ mac-cittaḥ karmānuṣṭhāna-kāle ‚nyadāpi māṃ smaran bhava

Baladeva

tādṛśatvād eva tvaṃ sarvāṇi sva-vihitāni karmāṇi kartṛtvābhimānādi-śūnyenacetasā svāmini mayi sannyasyārpayitvā mat-paro mad-eka-puruṣārtho mām eva buddhi-yogam upāśritya satataṃ karmānuṣṭhāna-kāle mac-citto bhava | etac ca tvāṃ prati prāg apy uktaṃ yat karoṣīty ādinā arpayitvaiva karmāṇi kuru, na tu kṛtvārpayeti