3.1 The Product and Quotient Rules & 3.2 The Chain Rule and the General Power Rule

Let’s take a minute to recall the rules we have so far for differentiation.

Constant-Multiple Rule (k is a constant) Sum Rule General Product Rule (r is a non-zero constant)

Some New Differentiation Rules Product Rule Quotient Rule

Chain Rule 1.When applying the chain rule, begin by identifying f(x) and g(x). 2.To differentiate f(g(x)), first differentiate the outside function f(x) and substitute g(x) for x in the result. Then, multiply by the derivative of the inside function g(x). Note: The General Power Rule we have been using is a special case of the chain rule. Why?

Alternate Notation for the Chain Rule Given the function y = f(g(x)), set u = g(x) so that y = f(u). With this notation we have y = f(u) and we note that Using this notation, the chain rule states that