Differentiation Techniques

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. Why…

Power Rule Implies Chain Rule

Having developed the Product Rule  and the Power Rule  for derivatives in your class, you can explore similar rules for the product of more than two functions and suddenly the Chain Rule will appear. For three functions use the associative property of multiplication with the rule above: So expanding with a slight change in notation: For…

The Derivative Rules I

The time is approaching when you will want and need to find derivatives quickly. I am afraid that, with the exception of the product rule, I have no particularly clever ideas of how to how to teach this. I am inclined to offer some explanation, short of a lot of proofs, to students as to…