Hun er dygtig til at spille violin.

In Danish, dygtig til is the normal pattern for saying someone is good at a particular activity.

• dygtig = skilled, capable
• til = the preposition that connects it to the activity

So:

• Hun er dygtig. = She is skilled / capable.
• Hun er dygtig til at spille violin. = She is good at playing violin.

This works like English good at, where you also need a preposition.

Dygtig usually means skilled, competent, or good because of ability.

In this sentence, it focuses on her skill at playing the violin.

Danish also uses god til in many similar cases:

• Hun er god til at spille violin.
• Hun er dygtig til at spille violin.

Both are possible, but dygtig often sounds a bit more like technically skilled / capable, while god is broader and more general.

Because at spille is the infinitive form, like English to play.

So:

• spille = play
• at spille = to play

After dygtig til, Danish commonly uses at + infinitive when the activity is expressed as a verb:

• dygtig til at synge = good at singing
• dygtig til at lave mad = good at cooking
• dygtig til at spille violin = good at playing violin

In Danish, musical instruments are usually used directly after the verb spille, without a preposition:

• spille violin
• spille klaver
• spille guitar

That is the normal idiomatic pattern.

So Hun er dygtig til at spille violin is the natural way to say it.

Because in Danish, when talking about playing an instrument, you usually do not use an article.

Compare:

• spille violin = play violin / play the violin
• spille klaver = play piano
• spille guitar = play guitar

This is different from English, which often says play the violin. Danish normally leaves out the article here.

Here is a simple breakdown:

• Hun = subject pronoun (she)
• er = present tense of være (is)
• dygtig = adjective (skilled / good)
• til = preposition
• at spille = infinitive phrase (to play)
• violin = noun (violin)

So the structure is basically:

subject + verb + adjective + preposition + infinitive phrase

Because Danish main clauses normally follow the V2 rule: the finite verb usually comes in the second position.

Here the sentence begins with the subject:

• Hun | er | dygtig til at spille violin.

So er comes second, which is exactly what Danish expects in a normal statement.

If you moved something else to the front, the verb would still stay in second position:

• Til koncerter er hun dygtig til at spille violin.

That V2 pattern is very important in Danish.

Yes, but it means something slightly different.

• Hun er dygtig til at spille violin.
  = She is good at playing the violin.
  This describes her overall ability.

• Hun spiller violin godt.
  = She plays the violin well.
  This focuses more directly on the action/performance.

They are close in meaning, but not identical in emphasis.

Yes. Danish can also use til with a noun phrase, depending on what you want to say.

For example:

• Hun er dygtig til musik. = She is good at music.
• Hun er dygtig til violin. = She is good at violin.

But Hun er dygtig til at spille violin is more specific, because it clearly says the skill is playing the violin.

You put ikke after the finite verb er:

• Hun er ikke dygtig til at spille violin.

This is the normal word order for negation in a main clause.

You mainly change the form of være:

• Hun er dygtig til at spille violin. = She is good at playing the violin.
• Hun var dygtig til at spille violin. = She was good at playing the violin.
• Hun har været dygtig til at spille violin. = She has been good at playing the violin.

The infinitive part at spille violin stays the same.

In most cases, yes.

• hun = she
• ham = him
• hende = her

But the exact English translation can depend on context. Grammatically here, hun is simply the third-person singular subject pronoun: she.

Dygtig changes depending on the noun or pronoun it describes.

Examples:

• Hun er dygtig. = She is skilled.
• Han er dygtig. = He is skilled.
• Barnet er dygtigt. = The child is skilled.
  (neuter singular adds -t)
• De er dygtige. = They are skilled.
  (plural adds -e)

In your sentence, hun is common gender singular, so the form is dygtig.

Yes, very much so.

The pattern:

[person] + er + dygtig/god til + at + verb

is extremely common in everyday Danish.

Examples:

• Han er god til at lave mad. = He is good at cooking.
• Jeg er dygtig til at lære sprog. = I am good at learning languages.
• De er gode til at samarbejde. = They are good at cooperating.

So Hun er dygtig til at spille violin is a completely natural sentence.