Introductory Calculus, Fall 2006, Dr. LeMesurier

Study Suggestions and Suggested Exercises for Chapter 3, Differentiation Rules

We will cover all sections of Chapter 3 except 3.9, omitting some parts of other sections as noted below.

Test 2 will cover this chapter.

Section 3.1 Derivatives of Polynomials and Exponential Functions, exercises 3, 5, 7, 8, 19, 23, 29.

Section 3.2 The Product and Quotient Rules, exercises 1, 3, 5, 7, 9, 11, 13, 23.

Section 3.3 Rates of Change in the Natural and Social Sciences, exercises 1, 3, 13 and 27. We did the applications to Physics and Economics only.

Section 3.4 Derivatives of Trigonometric Functions, exercises 1, 3, 5, 8, 11, 13, 16-19.

Section 3.5 The Chain Rule (Derivative of Compositions), exercises 1, 3, 5, 9, 11, 13, 31, 39, 43, 51.

Section 3.6 Implicit Differentiation, exercises 1, 3, 5, 9, 11, 25, 29.
Study only up to Example 4; that is, omit "Derivatives of Inverse Trigonometric Functions", which is covered in Calculus II (Math 220).

Section 3.7 Higher Derivatives, read up to Example 3 and look at exercises 1, 3, 5, 9, 21 and 27. (There is no need to know the name jerk, and we did not compute higher derivatives with implicit differentiation.)

Section 3.8 Derivatives of Logarithmic Functions, exercises 1, 3, 5, 15; plus 35 and 41 on Logarithmic Differentiation.
Study up to "Logarithmic Differentiation" and Example 8, but omit the final sub-section on "The Number e as a Limit".

Section 3.9 is omitted. It is covered in Calculus II.

Section 3.10 Related Rates, exercises 1, 3, 5, 7 and 9, and choose almost any others for practice. It is worth practicing this a lot, as it combines a number of useful ideas, like implicit differentiation and the various derivative rules, and recalling various geometric and trigonometric formulas. Remember that such "pre-calculus" formulas can be on a formula sheet for the test.

Section 3.11 Linear Approximations and Differentials, exercises 5, 9, 17, 21, 25. Omit Example 1 and exercises of that type: do only the examples and exercises that involve exact derivatives of functions.


© 2006 Brenton leMesurier, College of Charleston, Department of Mathematics.
Revised October 17, 2006.