Hi - These rules are given in the partitive articles lesson (it's 14.5 in Premium Plus), but they work similarly:
du - Masculine singular
de la - Feminine singular
de l’ - Masculine or feminine in front of a vowel or silent H
des - Masculine or feminine plural
It's *de l'étudiant* because étudiant starts with a vowel, so you get the "de le" étudiant contracted to de l'étudiant.
It's *du chien* because it's formed from "de le" chien, which is not contracted, so "de le" becomes "du".
Du vs De in French | De vs Du in French