mitnehmen
to take along
To take or transport someone or something with you from one place to another.
Kannst du mich auf dem Weg zur Arbeit mitnehmen?
Can you take me along on your way to work?

to take along / take away
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to take along
To take or transport someone or something with you from one place to another.
Kannst du mich auf dem Weg zur Arbeit mitnehmen?
Can you take me along on your way to work?

'Mitnehmen' (to take along) is a separable verb. In a main clause, the prefix 'mit' goes at the end of the sentence. In subordinate clauses and infinitive constructions, the verb stays together.
Ich nehme auf dem Weg zur Party noch Getränke mit.
I'll take some drinks along on the way to the party.
The verb is made up of the prefix 'mit-' and the verb 'nehmen' (to take). The prefix 'mit-' means 'together with' or 'along' and gives the verb its characteristic meaning of taking something or someone with you.
Nimm dir eine Jacke mit, es könnte später kalt werden.
Take a jacket along; it might get cold later.
In this meaning, the fixed expression 'zum Mitnehmen' (to take away / to go) is often used. For example, you might order 'einen Kaffee zum Mitnehmen' (a coffee to go).
Alle Gerichte auf der Karte gibt es auch zum Mitnehmen.
All dishes on the menu are also available to take away.
In this figurative meaning, the person who is emotionally or physically affected is the accusative object. The subject is the event or thing that causes the strain.
Der Tod seines Haustieres hat das Kind sehr mitgenommen.
The death of his pet really wore the child out.
When gaining an insight, the preposition 'aus' (from) is often used to name the source of the experience. Typical formulations are 'etwas aus einer Situation mitnehmen' (to take something away from a situation) or 'eine Lektion mitnehmen' (to take away a lesson).
Aus diesem Fehler habe ich eine wichtige Lektion mitgenommen.
I took away an important lesson from this mistake.
at / with / near
'bei sich haben' and 'mitnehmen' are both connected to having something with you. The difference lies in the perspective. 'Bei sich haben' describes the state: you have something with you right now. 'Mitnehmen' describes the action: you take something from one place to another. Learners can confuse this because in both cases an object is with a person. If you want to say that something is now in your bag, 'bei sich haben' fits. If you are saying that you pack it or transport it, 'mitnehmen' fits.

Am Bahnhof nehme ich meinen Rucksack mit in den Zug.
At the station, I take my backpack with me onto the train.
Frau Yilmaz hat ihren Ausweis immer bei sich.
Ms. Yilmaz always has her ID with her.