Learn Dutch: Uit het experiment moet je de waarheid kunnen afleiden. - From the experiment you must be able to deduce the truth.

No, in this context moeten is used for logical deduction, not obligation. It means "it is logically expected" or "it has to be the case." The sentence is saying that the experiment logically should make it possible to find the truth, rather than ordering you to do it.

Why does the sentence say moet je instead of je moet?

Because the sentence starts with the prepositional phrase Uit het experiment. In Dutch, whenever a main clause starts with anything other than the subject, the verb and subject swap places (this is called inversion). The conjugated verb moet must stay in the second position.

Why are there two verbs, kunnen and afleiden, stacked at the end?

When you use a conjugated modal verb like moeten, any other verbs in the clause get pushed to the end as infinitives. Here we have two: kunnen (to be able to) and afleiden (to deduce). Dutch groups these infinitives together at the very end of the sentence.

Afleiden is a separable verb (af + leiden). Why isn't it separated here?

Separable verbs only split when they act as the conjugated verb in the sentence (for example: Ik leid de waarheid af). Because moet is the conjugated verb here, afleiden is pushed to the end and remains in its full, unseparated infinitive form.