Efter en opdatering virker appen heldigvis bedre.

Because efter means after, and en opdatering means an update. Together, Efter en opdatering means After an update.

Danish often puts a time phrase first in the sentence. That changes the word order in the rest of the sentence.

Because opdatering is a common-gender noun in Danish, so it takes en in the indefinite singular.

• en opdatering = an update
• opdateringen = the update

This is something you usually just have to learn with the noun.

Here, virker means works, is working, or more naturally in this context, functions.

The verb is at virke.

Examples:

• Appen virker. = The app works.
• Det virker ikke. = It doesn’t work.

In this sentence, virker ... bedre means works better or is working better.

Appen is the normal Danish way to say the app. Danish usually adds the definite article as an ending to the noun.

• en app = an app
• appen = the app

Using den app is possible in some contexts, but it usually needs an extra reason, such as emphasis or additional description:

• den nye app = the new app

So in this sentence, appen is the natural choice.

Because Danish uses verb-second word order in main clauses.

When the sentence starts with something other than the subject, the finite verb still has to come in the second position.

So:

• Normal order: Appen virker heldigvis bedre.
• With a time phrase first: Efter en opdatering virker appen heldigvis bedre.

Structure:

1. Efter en opdatering
2. virker
3. appen
4. heldigvis
5. bedre

This is a very important Danish pattern.

Heldigvis means fortunately or luckily.

In this sentence it comments on the whole situation: fortunately, the app works better now.

Its position is very natural in Danish. It often comes after the subject when the verb is in second position:

• Efter en opdatering virker appen heldigvis bedre.

You could also hear similar placement in other sentences:

• Han er heldigvis hjemme. = He is fortunately at home.

Bedre is the comparative form of god (good) in the sense of better.

It is irregular, just like English:

• god = good
• bedre = better
• bedst = best

But here bedre is modifying how the app works, so in English the most natural translation is better, not more good.

Not directly. Bedre literally means better.

So:

• Appen virker bedre. = The app works better.

If you want to say the app is improved, Danish would usually use a different structure, for example:

• Appen er blevet bedre. = The app has gotten better / improved.

In your sentence, the focus is specifically on performance or functioning.

Yes. Virker is the present tense form of at virke.

• at virke = to work / function
• virker = works / is working

Even though English often uses is working better in this kind of context, Danish simple present is completely normal here.

Yes, but the meaning changes slightly.

• Efter en opdatering = After an update
  This sounds more general or introduces an update without specifying which one.

• Efter opdateringen = After the update
  This refers to a specific update that both speaker and listener know about.

So both are correct, but they are not exactly the same.

Danish often leaves that idea implied when the context already makes it clear.

Efter en opdatering virker appen heldigvis bedre naturally suggests that after the update, the app works better now than before.

If you wanted to make now explicit, you could say:

• Efter en opdatering virker appen heldigvis bedre nu.

But it is not necessary.

Exactly as written: Efter en opdatering virker appen heldigvis bedre. It sounds natural and idiomatic.

A few close alternatives are also possible:

• Appen virker heldigvis bedre efter en opdatering.
• Efter opdateringen virker appen heldigvis bedre.

The original sentence is completely normal Danish.

A rough English-friendly guide would be something like:

ohb-deh-teh-ring

But Danish pronunciation is tricky, and the real sounds are softer and more reduced than English spelling suggests.

A few helpful notes:

• -ing in Danish is not pronounced exactly like English -ing
• unstressed syllables are often weaker
• d can sound softer than an English d

So the written form is easy to learn, but the spoken form takes practice.