See also Category:Differentiation rules for a list of all the differentiation rules pages (including pages for higher derivatives, which are not in this table).
Qualitative and existential questions
Generic point computation questions
Predicting when things become zero
The questions here can be done in two ways. The first is to use the abstract differentiation rules to figure things out. The second is to actually determine the possibilities for the functions at hand, and then figure out what we can say about their sums, products, and composites.