what's the purpose of "au" in this sentence? Would it be wrong to say "Vous ne jouez pas tennis"
the verb is "jouer à" for sports (jouer de for musical instruments)
je joue au tennis
je joue au volley
je joue au football
So, yes, it's wrong to leave à out
Many French verbs take prepositions where the English equivalent verb doesn't (and sometimes the other way round). When you learn a new verb it's always a good idea to learn its corresponding preposition (if it has one)
In other negatives it becomes "de" for "any," why is it not the case here? Thanks
The rule is that in a negative sentence where the noun is the direct object of the verb being negated, de is commonly used instead of an indefinite or partitive article (un, une, du, de la, and des).
Je n'ai pas de chien. - I don't have a dog.
Pas de problème. - Not a problem.
je ne veux pas d’eau - I don’t want any water