Der Arzt untersucht das Gehirn.

Because der Arzt is the subject of the sentence — the person doing the action.

In Der Arzt untersucht das Gehirn, the doctor is the one performing the examination, so Arzt is in the nominative case.

• der Arzt = the doctor (subject / nominative)
• den Arzt = the doctor (direct object / accusative)

So:

• Der Arzt untersucht ... = The doctor examines ...
• Ich sehe den Arzt. = I see the doctor.

Because Gehirn is a neuter noun in German, so its nominative and accusative definite article is das.

Here it is also the direct object — the thing being examined.

• das Gehirn = the brain

In this sentence, das Gehirn is accusative, but for neuter nouns the article das stays the same in both nominative and accusative:

• nominative: das Gehirn
• accusative: das Gehirn

That is why you do not see a change here.

In this sentence:

• Der Arzt = subject
• untersucht = verb
• das Gehirn = direct object

You can identify them by both meaning and case marking:

• der shows nominative masculine, which often marks the subject
• das here is the object being acted on

A useful question is:

• Who is doing the action? → der Arzt
• What is being examined? → das Gehirn

So the structure is:

Subject + verb + object

Untersucht is the third person singular present tense form of the verb untersuchen.

Conjugation in the present tense:

• ich untersuche
• du untersuchst
• er/sie/es untersucht
• wir untersuchen
• ihr untersucht
• sie/Sie untersuchen

Since der Arzt means he / the doctor, the correct form is untersucht.

No, untersuchen is not separable.

That means it stays together:

• Der Arzt untersucht das Gehirn.

It does not split like a separable verb would.

For comparison:

• separable: anrufen → Ich rufe den Arzt an.
• inseparable: untersuchen → Ich untersuche das Gehirn.

So untersuchen always remains one unit.

Because standard German main clauses usually follow the V2 rule: the finite verb goes in the second position.

In this sentence:

1. Der Arzt
2. untersucht
3. das Gehirn

That is a normal German main-clause pattern.

Even if you move another element to the front, the verb still stays second:

• Das Gehirn untersucht der Arzt.

This version is less neutral and puts more emphasis on das Gehirn, but the verb still stays in second position.

Yes. That changes the meaning slightly:

• Der Arzt untersucht das Gehirn. = The doctor is examining the brain.
• Ein Arzt untersucht das Gehirn. = A doctor is examining the brain.

Use der when the doctor is definite or already known in context. Use ein when you mean a doctor in a more general or first-mentioned sense.

Because many masculine nouns in German do not take an ending in the nominative singular.

The base form is:

• der Arzt

However, in some other cases you may see changes in the article, and sometimes in formal German you may also see noun endings in certain patterns, especially in genitive or with weak nouns — but Arzt in everyday sentences usually looks like this:

• nominative: der Arzt
• accusative: den Arzt
• dative: dem Arzt
• genitive: des Arztes

So in this sentence, Arzt stays simply Arzt.

A rough guide:

• Arzt sounds approximately like ahrtst

A few notes:

• Ar is pronounced with an a like in father
• zt at the end is pronounced like tst
• the r is usually not strongly rolled in standard German pronunciation

So the whole word is compact and ends in a sharp consonant cluster.

A rough guide:

• Gehirn sounds approximately like guh-HEERN or geh-HEERN, depending on accent and how roughly you approximate it in English

Helpful points:

• the stress is on the second syllable
• ge- is unstressed
• hirn contains a long ee-like sound before the final consonants

The exact German sound is better learned by listening, but the key thing is: ge-HIRN, with stress on HIRN.

Yes. The German present tense often covers both simple present and present progressive meanings.

So:

• Der Arzt untersucht das Gehirn.

can mean:

• The doctor examines the brain.
• The doctor is examining the brain.

The exact meaning depends on context. German usually does not need a special form like English is examining.

This is the most neutral and common order:

• Der Arzt untersucht das Gehirn.

German does allow other word orders, especially to emphasize certain parts, but the case markings and the verb-second rule help keep the sentence understandable.

For example:

• Das Gehirn untersucht der Arzt.

This is grammatically possible, but it sounds more marked and emphasizes das Gehirn.

For learners, the safest default is:

Subject + verb + object

It is in the accusative case, because it is the direct object of untersucht.

The verb untersuchen normally takes a direct object:

• jemanden / etwas untersuchen = to examine someone / something

So here:

• subject: der Arzt
• verb: untersucht
• accusative object: das Gehirn

Even though das looks the same in nominative and accusative, its role here is accusative because it receives the action.