Some people slip up when trying to use or recognize partitive articles because they look identical to other words with different meanings.

The following is a partitive article, for instance:

Ma grand-mère met du cognac dans ses gâteaux.
My grandma puts (some) brandy in her cakes.

But the following is not:

La couverture du livre est grotesque.
The cover of the book is grotesque.

In the second example, the 'du' is merely a contraction of de + le (preposition [of] + definite article [the]).

"De l'audace, encore de l'audace,
toujours de l'audace. "
Non, c'est le portefeuille de l'homme en face.
No. It's the wallet of the man across the way.

Notice how the partitive article and its noun can stand alone as an independent unit, whereas the preposition and article combination links together two nouns.

Il y a de la sagesse dans votre lettre.
There is (some) wisdom in your letter.

Tante Em est la soeur de la mère de Dorothy.
Aunt Em is the sister of the mother...
Tiens ! il y a des fourmis sur ton sandwich.
Look! There are (some) ants on your sandwich.
On appelait Louis-Philippe le roi des Français.
Louis-Philippe was called king of the French.