This website out of the University of Tennessee, Knoxville, provides examples of using derivative shortcuts as well as A LOT of practice problems on using derivative shortcuts. Answers are provided. This is a great resource as you prepare to take the Derivative Gateway Exam.
"The 17 equations that changed the world." -- Business Insider article (Based on a book with that name by Ian Stewart.)
"The 10 equations that changed biology." -- Short Bioscene article by John Jungck