## Mathematics 101## Calculus I |

*Chapter 3: Differentiation Rules*

- 3.1 Derivatives of Polynomials and Exponential Functions (pdf)
- 3.2 The Product and Quotient Rules (pdf)
- 3.3 Rates of Change in the Natural and Social Sciences (pdf)
- 3.4 Derivatives of Trigonometric Functions (pdf)
- 3.5 The Chain Rule (pdf)
- 3.6 Implicit Differentiation (pdf)
- 3.7 Derivatives of Logarithmic Functions (pdf)
- 3.8 Linear Approximation and Differentials (pdf)
- Review of Chapter 3 (pdf)

- 3.1 -- 1 (the number e), 11, 13, 19, 25, 27, 32, 36, 41 (motion), 44, 50 (parallel lines), 58 (differential equation), 65
- 3.2 -- 1, 2 (two ways), 3, 5, 9, 15, 21, 23 (Maria Agnesi), 31, 33, 36, 39 (income), 41, 43 (how many?)
- 3.3 -- 1, 3, 4 (speeding up), 8 (ball), 10 (sodium chlorate crystals), 14 (spherical cell), 20 (lactonization), 26 (violin string), 30 (sensitivity), 32 (fish farm), 33 (wolves and caribou)
- 3.4 -- 3, 7, 18, 23, 29, 31 (spring), 33 (ladder), 37 (differential equation)
- 3.5 -- 5, 9, 15, 19, 25, 29, 36, 37, 43, 45, 46, 61 (cepheid variable), 63 (friction), 64 (rumor), 68 (exponential population growth), 73 (parametric curves), 76 (CAS)
- 3.6 -- 1, 7 (implicit differentiation), 17 (cardioid), 24 (bouncing wagon), 31, 41 (steepest descent), 42 (isobars), 49 (rotated ellipse)
- 3.7 -- 1 (why the natural log?), 3, 7, 17, 21, 24, 26, 31 (logarithmic differentiation)
- 3.8 -- 1 (turkey), 2 (atmospheric pressure), 3 (Australia's population), 4 (Nepal's population), 9 (linear approximation), 13 (accuracy), 24 (differential), 30 (paint), 31 (Poiseuille's Law)

Use the following exercises to review and test your understanding of the material in Chapter 3. This is not homework, and there is nothing to hand in from this activity.

- Review Exercises, Chapter 3, pp. 255--257 -- 5, 7, 13, 19, 21, 27, 31, 36, 43, 45, 48, 51, 59, 62, 64, 69, 71, 73

The following links are to pdf files. They can be viewed with an application such as Adobe Acrobat Reader.

- Handout: Calculating Derivatives pdf

The following Mathematica notebooks are available in two formats. Download the Mathematica notebooks (nb) to your machine and use Mathematica to interpret their contents, or click on the web page link (html) to see a static image of the evaluated notebook.

- 3.1 The Derivatives of Polynomials and Exponential Functions nb html
- 3.2 The Product and Quotient Rules nb html
- 3.3 Rates of Change in the Natural and Social Sciences nb html
- 3.4 Derivatives of Trigonometric Functions nb html
- 3.5 The Chain Rule nb html
- 3.6 Implicit Differentiation nb html
- 3.7 Derivatives of Logarithmic Functions nb html
- 3.8 Linear Approximations and Differentials nb html