Comment by alexvr

Actually, most algebraic tricks in calculus, which are what make it challenging, are pretty unnecessary to know if you can program a computer or use existing math software. Conceptual tricks, on the other hand, which might be more aptly called "conceptual applications," should be understood and derived. The unfortunate thing is that many students get so accustomed to memorizing tricks that would indeed require really advanced math abilities and lots of time to derive that they gloss over valuable concepts that they should actually understand very well.