Learn Hardcore Norwegian: Hun er tydeligvis trøtt i dag.

Hun = she (subject pronoun).
er = is (present tense of å være = to be).
tydeligvis = obviously/evidently (a sentence adverb expressing the speaker’s inference).
trøtt = tired (predicative adjective describing the subject).
i dag = today (time adverbial).

How do I pronounce it?

IPA (one common Oslo-like pronunciation): [hʉn ær ˈtỳːdəlɪˌviːs trœtː iː ˈdɑːɡ]
Rough guide: hun ≈ HOON (with a tight, rounded u), er ≈ air (tapped r), tydeligvis ≈ TY-deh-lee-vees, trøtt ≈ trut (ø like French peur or German schön), i dag ≈ ee daag.

Why is tydeligvis after er?

Norwegian main clauses follow the verb-second (V2) rule: the finite verb (er) must be in the second position. Sentence adverbs like tydeligvis typically come right after that verb: Hun [1] er [2] tydeligvis [3] ….

Can I move tydeligvis to other positions?

Yes, with slight changes in emphasis:

I dag er hun tydeligvis trøtt. (Topicalizes “today.”)
Tydeligvis er hun trøtt i dag. (Fronted adverb; more formal/emphatic.)
Hun er trøtt i dag, tydeligvis. (End-position comment; more afterthought-like.) All are grammatical; the original is the neutral default.

What’s the difference between tydeligvis and tydelig?

tydeligvis is a sentence adverb meaning “obviously/evidently” (speaker’s inference): Hun er tydeligvis trøtt i dag.
tydelig is an adjective/adverb meaning “clear/clearly” (about how something appears): Hun er tydelig trøtt i dag ≈ “she is clearly/visibly tired today.” The first highlights your conclusion; the second highlights how it appears.

How does tydeligvis compare to sikkert, visst, and åpenbart?

tydeligvis: evidently/obviously based on signs you perceive (inference).
sikkert: probably/most likely (probability, not necessarily visible signs).
visst: apparently/indeed (can sound conversational; also means “indeed” in some contexts).
åpenbart: obviously; often a bit stronger or more formal than tydeligvis. Examples: Hun er sikkert trøtt (she’s probably tired), Hun er visst trøtt (she’s apparently/it seems she’s tired), Hun er åpenbart trøtt (she’s obviously tired).

Where does ikke go, and how does it affect meaning?

Hun er tydeligvis ikke trøtt i dag. = It’s obvious that she is not tired today (obviously not tired).
Hun er ikke tydeligvis trøtt i dag. = She is not obviously tired today (it isn’t obvious). Both are grammatical but mean different things.

Why is i dag two words? Is idag wrong?

Standard Norwegian writes it as two words: i dag. The same goes for i går (yesterday) and i morgen (tomorrow). The one-word forms are non-standard in modern Bokmål.

Could I say i dagen?

Not for “today.” i dagen would mean “in the day” (literal, unusual in modern usage). For “during the day,” use om dagen or på dagtid. “Today” is always i dag.

Does trøtt agree with the subject?

Yes. Predicative adjectives agree in number (and sometimes neuter), but trøtt already ends in -t, so neuter looks the same.

Singular: Hun er trøtt. / Barnet er trøtt.
Plural: De er trøtte.

What’s the nuance difference between trøtt, sliten, and søvnig?

trøtt: tired (often need of rest/sleep; general).
sliten: worn out/exhausted (from effort; physically/mentally drained).
søvnig: sleepy/drowsy (about to fall asleep).

Is Hun always right here? What about henne, ho, or hen?

Hun is the subject form (she) and is correct here.
henne is the object form (her).
ho is common in many dialects and standard in Nynorsk; not standard Bokmål.
hen is a gender-neutral third-person singular pronoun increasingly used in Bokmål.

Can I say Hun er veldig trøtt i dag instead? Does it mean the same?

Hun er veldig trøtt i dag. = She is very tired today (degree/intensity).
Hun er tydeligvis trøtt i dag. = It’s obvious/evident she’s tired (speaker inference). You can combine them: Hun er tydeligvis veldig trøtt i dag.

How would this look in past or perfect tense?

Hun var tydeligvis trøtt i går. (was)
Hun har tydeligvis vært trøtt i det siste. (has been) The sentence adverb still comes right after the finite verb (var/har).

What happens in a subordinate clause?

In subordinate clauses, sentence adverbs come before the verb (no V2):

Jeg tror (at) hun tydeligvis er trøtt i dag. Here tydeligvis precedes er.

Are there natural alternatives to express the same idea?

Yes:

Det er tydelig at hun er trøtt i dag. (It is clear that…)
Hun virker trøtt i dag. (She seems tired today.)
Hun ser trøtt ut i dag. (She looks tired today.) These avoid the sentence adverb but convey a similar assessment.