Chapter 2.2 - Basic Differentiation Rules and Rates of Change

Objectives:

• • Find the derivative of a function using the Constant Rule.

  • Find the derivative of a function using the Power Rule.

  • Find the derivative of a function using the Constant Multiple Rule.

  • Find the derivative of a function using the Sum and Difference Rules.

  • Find the derivative of the sine function and of the cosine function.

  • Use derivatives to find rates of change.

Basic Differentiation pt1 (for Day #3 lesson)

Getting accustomed to the basic differentiation rules: power rule, sum/difference rule, constant multiple rule. Also, see how simplifying the function algebraically BEFORE differentiating can often make your job much easier.

Basic Differentiation pt2 (for Day #4 lesson)

Using basic differentiation rules to find the slope of a graph at an indicated point, and also find the tangent line equation.

Basic Differentiation pt3, Free-fall motion (for Day #4 lesson)

Basic differentiation as applied to a "free-fall motion" exercise (a body  subjected to no force other than gravity).

Practice for the Multiple Choice Assessment on Chapters 1.1-2.2

Calculator NOT allowed for this assessment. 

As shown in class today, here are types of questions you'll see:

• • Various limit problems

  • PreCalc stuff related to limits (e.g. asymptotes)

  • Limit definition of derivative

  • "Shortcuts" for derivative (e.g. power rule)

  • Derivatives requiring rewriting/simplifying

  • Find equation of the tangent line...

  • Where is a graph differentiable?

In the Barron's AP Prep book (2025 edition), you should know how to do the following Multiple Choice exercises. Practicing these exercises is your best way to prepare for the upcoming Multiple Choice assessment. Questions listed in grey and in parentheses are ones that you should know how to do at this point, but I won't include any like them on THIS test. Fair game next time though!

• • "Limits and Continuity" chapter (p90 in 2025 edition):

    • All exercises, except those involving limits as x approaches +/- infinity. You may find that your PreCalc knowledge will allow you to even do many of those, but we won't officially cover those in Calculus until a little later in the course:

    • A1, A3, A4, (A5), A11, A12, (A13), A14, A15, (A16), A17, A19, A21, A22, A23, A24*, (A25), (A26), A27
      * The 2025 edition of Barron's book A24 has a typo. The part of the piecewise function that says f(2) = -3 SHOULD say f(1) = -3. Oddly, this error did not exist in earlier editions of the book.

    • B1, B2, B4, B5, B6, B7, B8, B9, B11, B13, B14, B15

  • "Differentiation" chapter (p121 in 2025 edition):

    • We're still early in our differentiation skills, so just the following:

    • (A3), (A4), A5, A6, A26, A35, A36, A38, (A42), A46, A47, A48, A49, (A52)

    • B11, B14, B15, (B16), (B17), (B24), B25, B33, B34, (B35), B36, (B37)

If you find all of these Limit and Differentiation exercises to be do-able, then you should be in good shape. Reminder that the answers immediately follow the exercises, including brief explanations for each one.

Go to next page, Chapter 2.3.