"What is this woman doing?"

Translation: Vad gör denna kvinna?

[kaplein]

Why are both denna kvinna and denna kvinnan correct?

[Zmrzlina]

Because both reflect how Swedes speak, although denna + definite noun is discouraged in formal writing.

[kaplein]

Thanks!

[jarrettph]

I thought that was flat out wrong.

[Arnauti]

Svensk ordbok says it's acceptable in written texts that are "not overly formal". denna kvinna does sound a bit too formal for most occasions.
With den här though, only the definite form is possible.

[Joshua118516]

What's the purpose for the "den här" alternative to "denna"?

[jarrettph]

Thanks for clarifying.

[jarrettph]

Could you say Vad håller den här kvinnan på med?

[Arnauti]

Yes, definitely.

[Patrick889093]

Why denna and not de här for this?

[InvertedGo]

Because it's one woman and not many. You would say Vad gör de här kvinnorna? but that would, of course, not match the meaning of the English sentence.

[MONTLIBAN]

In the previous question it was detta man and here it is denna kvinna. Any suggestions?

[EwaDuVarra]

same question ......

[MONTLIBAN]

I think Duo should be more lenient. After all we are not studying Sweish to write books. Just to get along in everyday conversation.