So, no one wants to do complicated limits to find derivatives. There are easier ways of course. There are a number of quick ways (rules, formulas) for finding derivatives of the Elementary Functions and their compositions. Here are some ways to introduce these rules; these are the subject of this week’s review of past posts.
The Derivative I Guessing the derivatives from the definition
The Derivative II Using difference quotients to graph and guess
The Derivative Rules I The Power Rule
The Derivative Rules II Another approach to the Product Rule from my friend Paul Foerster
The Derivative Rules III The Quotient Rule developed using the Power Rule, an approach first suggested by Maria Gaetana Agnesi (1718 – 1799) who was helping her brother learn the calculus.
Next week: The Chain Rule.
Revised from 9-12-2017