
nachkommen
to follow later
To follow someone to a place or arrive there later than others.
Geht ihr schon mal ins Restaurant, ich komme in zehn Minuten nach.
You go ahead to the restaurant; I'll follow later in ten minutes.
to follow later / comply
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to follow later
To follow someone to a place or arrive there later than others.
Geht ihr schon mal ins Restaurant, ich komme in zehn Minuten nach.
You go ahead to the restaurant; I'll follow later in ten minutes.

to comply with
To fulfill a duty, request, demand, or obligation.
Der Händler ist seiner Verpflichtung zur Lieferung der Ware nicht nachgekommen.
The dealer did not comply with his obligation to deliver the goods.

to keep up
To be able to keep pace or manage the amount of work. Often used in the negative.
Wir haben so viele Bestellungen, dass ich mit dem Verpacken kaum noch nachkomme.
We have so many orders that I can hardly keep up with the packing anymore.
'Nachkommen' (to follow later / comply) is a separable verb. In a main clause, the prefix 'nach-' goes at the end. In a subordinate clause or infinitive, the verb stays together.
Ich komme später zur Feier nach.
I'll follow later to the party.
Since 'nachkommen' (to follow later / comply) describes movement or a change, the perfect tense is always formed with the auxiliary verb 'sein'.
Sie ist erst eine Stunde später nachgekommen.
She followed later only an hour afterward.
In the meaning 'to fulfill', 'nachkommen' (to comply with) always requires an object in the dative. You comply with 'einer Sache' (something).
Bitte kommen Sie unserer Aufforderung umgehend nach.
Please comply with our request immediately.
In the meaning 'to keep up', 'nachkommen' (to keep up) is very often negated or used with adverbs like 'kaum' (hardly). It often appears with the preposition 'mit' and a dative object.
Ich komme mit dem Lesen der E-Mails gar nicht mehr nach.
I can't keep up with reading the emails at all anymore.
to follow
Both verbs can express that someone responds to an instruction or other directive. Folgen is used especially with instructions, rules, or advice; nachkommen emphasizes fulfilling a request, demand, or duty. Therefore, one is more likely to folgt einer Anweisung and kommt einer Bitte oder Verpflichtung nach.

Mia kommt der Bitte nach und wartet vor der Tür.
Mia complies with the request and waits outside the door.
Mia folgt der Anweisung und wartet vor der Tür.
Mia follows the instruction and waits outside the door.