Kan De logge ind med det link, som læreren har sendt?

De is the formal, polite form of you in Danish. It is traditionally capitalized to show respect.

So:

• De = formal you
• du = informal you

In modern Danish, du is much more common in everyday life, and De can sound very formal, old-fashioned, or especially polite depending on the context.

So this sentence is more polite than:

• Kan du logge ind med det link, som læreren har sendt?

Because this is a yes/no question.

In Danish, yes/no questions usually begin with the finite verb. Here, the finite verb is kan.

Compare:

• Statement: De kan logge ind ...
• Question: Kan De logge ind ... ?

This is similar to English:

• You can log in ...
• Can you log in ... ?

Logge ind is a verb expression meaning to log in or to sign in.

A few useful points:

• at logge ind = to log in
• After a modal verb like kan, Danish normally uses the infinitive without at

So:

• Kan De logge ind ... ? = correct
• not Kan De at logge ind ... ?

This works like English:

• can log in
• not can to log in

Because link is a neuter noun in Danish.

Its basic form is:

• et link

Since it is an et-word, the matching demonstrative is det:

• det link = that link / the link in this context

If it were a en-word, you would use den instead.

So the agreement is:

• en noun → den
• et noun → det

Here med means with, but in context it really means using or by means of.

So:

• logge ind med det link = log in using that link

English often uses with or using in the same way.

You may also see other Danish wording in similar contexts, such as:

• via det link
• gennem det link

But med det link is completely natural.

Som is a relative pronoun here. It means that or which.

It introduces the relative clause:

• som læreren har sendt = that the teacher has sent

This clause describes det link.

So the structure is:

• det link = the link
• som læreren har sendt = that the teacher has sent

Unlike English, Danish usually keeps som in this kind of sentence. English can sometimes omit that, but Danish normally cannot omit som here.

Because som læreren har sendt is a subordinate clause, and subordinate clauses in Danish usually keep the order:

• subject + finite verb

So:

• læreren = subject
• har = finite verb
• sendt = past participle

That gives:

• som læreren har sendt

In main clauses, Danish often has verb-second word order, but after som you are inside a subordinate clause, so the word order changes.

Har sendt is the present perfect.

It is used for an action that happened in the past but is relevant now. That fits this sentence well: the teacher sent the link, and now the person is being asked to use it.

So:

• har sendt = has sent
• sendte = sent

Both can be possible in some contexts, but har sendt strongly connects the past action to the present situation.

Because læreren is the definite form of lærer.

• en lærer = a teacher
• læreren = the teacher

Danish often marks definiteness by adding an ending to the noun, instead of using a separate word like English the.

So in this sentence:

• læreren har sendt = the teacher has sent

Yes, absolutely. In fact, that would be more common in modern everyday Danish.

The informal version is:

• Kan du logge ind med det link, som læreren har sendt?

The difference is mainly tone:

• De = formal, polite, distant
• du = normal, everyday, informal

So if you are speaking to a student, colleague, or most people in modern Denmark, du is usually the natural choice.