Take a masculine noun for a person or animal, add -in, and you get the feminine counterpart. derLehrer becomes dieLehrerin. The article is always die, without any exceptions.
The rule
Whenever a masculine noun names a person or an animal, German can form the feminine equivalent by adding -in to the end. The base word doesn't disappear, it's still right there, just with a new ending and an article that is always die.
| Masculine | Feminine | Meaning |
|---|---|---|
| derLehrer | dieLehrerin | teacher |
| derStudent | dieStudentin | student |
| derFreund | dieFreundin | friend |
| derFahrer | dieFahrerin | driver |
Sometimes the base word changes too
Many masculine nouns take an umlaut when -in is added: a becomes ä, o becomes ö, au becomes äu. The suffix and the article rule don't change, only the vowel does.
| Masculine | Feminine | Meaning |
|---|---|---|
| derArzt | dieÄrztin | doctor |
| derKoch | dieKöchin | cook |
| derAnwalt | dieAnwältin | lawyer |
| derBauer | dieBäuerin | farmer |
The plural: -innen
Plural nouns are die in the Nominativ anyway, but -in words mark their plural with a second -in → die Lehrerinnen, die Ärztinnen, die Studentinnen, die Freundinnen. One teacher → die Lehrerin. Several → die Lehrerinnen. The doubled -in is the signal that you're looking at a group of women or a mixed reference to the feminine form.
Not every -in word is this suffix
The rule is specific. It applies when -in is added to a masculine person or animal noun to create its feminine form. It does not cover every word that happens to end in those two letters.
dasVitamin, dasBenzin → both neuter, both das. derCousin, derPinguin → both masculine, both der. dieMedizin → feminine, but for its own reasons, not because something was made feminine from it. In all of these, -in is part of the root, not a suffix added to a masculine noun.
How to spot one in the wild
Strip the -in (and undo the umlaut, if there is one) and ask: is what's left a real masculine noun for a person or animal? Lehrerin minus -in is Lehrer, a real masculine noun. Ärztin minus -in, with ä back to a, is Arzt, another real one. Vitamin minus -in is Vitam, not a word, so it's not this suffix. If the stripped-down form is a real masculine person or animal noun, the -in word is its feminine counterpart, and the article is die.
Masculine person or animal noun plus -in equals the feminine form, always die. Add a second -in for the plural. The umlaut can change, the article cannot.