Breakdown of Ты должен следовать по этому пути.
ты
you (singular)
этот
this [f: эта, n: это]
должен
must, have to (должен, должна, должны)
по
along, around
Questions & Answers about Ты должен следовать по этому пути.
Why does the masculine noun путь end in -и here? Shouldn't a masculine dative noun end in -ю?
This is exactly what makes путь an anomalous noun! Although it is masculine, it borrows most of its case endings from the 3rd declension—the pattern normally used for feminine nouns ending in a soft sign (like ночь). After the preposition по, we need the dative case, and the 3rd declension dative ending is -и, giving us пути.
If путь takes feminine endings, why is the demonstrative pronoun этому (masculine) instead of этой (feminine)?
Adjectives and demonstrative pronouns like этот always agree with a noun's inherent gender, regardless of what its declension pattern looks like. Because путь is a masculine noun, этот must take the standard masculine dative form, which is этому.
Why is the preposition по used here? Can't I just say следовать этот путь without it?
No, следовать (to follow) does not take a direct object in the accusative case like the English "follow" does. When you are physically following a road, route, or path, Russian requires you to use по + the dative case (essentially meaning "to proceed along the path").
How do we know the "you" in this sentence is a male, and what would it look like for a female?