CHAPTER 3
Derivative Rules and Tools
3.1 Derivatives of Polynomials and Exponentials
3.2 Product and Quotient Rules
3.3 Chain Rule and Implicit Differentiation
3.4 Derivatives of Trigonometric Functions
Figure 3.1 Differential calculus is used in Section 3.1 to model the rate at which HIV virions (as depicted) is cleared from the body during drug therapy.
Preview
“I loved history, but still loved science, and thought maybe you don't need quite as much calculus to be a biology major.”
Elizabeth Moon, science fiction writer (b. 1945) Part 2 of an interview with Jayme Lynn Blaschke November 1999; http://www.sfsite.com/02b/em75.htm
In the previous chapters we have only been able to compute derivatives by directly appealing to the definition of the derivative. As you may have noticed, computing derivatives in this manner quickly becomes tedious. In this chapter we consider the rules and tools that allow us to quickly compute the derivative of any imaginable function. Learning these rules is critical, as expressed in the following admonition (from Colin Adams, Joel Hass, and Abigail Thompson, How to Ace Calculus: The Streetwise Guide, New York: W. H. Freeman, 1998):
“Know these backwards and forwards. They are to calculus what ‘Don't go through a red light’ and ...
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