# Derivatives

**1) Average Rate of Change**

- Explanation:
- Notes | Annotated
- Video: what is a rate?
- Interactive websites for exploring the relationship of the average rate of change (secant lines) and the instantaneous rate of change (tangent lines):
- Teacherlink (flash)
- University of British Columbia - Math Labs: Secant Lines (Java - don't open in Chrome) - move the red point on top of the blue point to find the slope at
*x*= 0

- Practice

**2) Definition of a Derivative **

- Explanation:
- Notes | Annotated
- Videos:
- Kahn: Calculus: Derivatives 1 (new HD version) - general definition
- Kahn: Calculus: Derivatives 2.5 (new HD version) - find the derivative using the definition
- Hollis: The derivative (slides #1-5)

- Interactive Websites:
- http://www.univie.ac.at/future.media/moe/galerie/diff1/diff1.html#ableitung (look at the first applet to look at tangent line only; do not open in Chrome) - move the slider to see how the slope of the tangent line changes
- Tangent to a point on a curve (Shodor - Java); use the slider to change the point of tangency after you type in a function to a graph; the slope of the change line changes therefore the slope is a function of x.
- Khan Module: video explanation | Derivative Intuition: Tangent to a point on a curve (intuitive approach) and all of the slopes of the tangent lines creates a function

- Practice Problems:

**3) Power Rule (and sum/difference, and constant multiple rules)**

- Explanation:
- Notes | Annotated
- Khan video: Calculus: Derivatives 3: Determining the derivatives of simple polynomials.

- Practice:
- Worksheet | Answers
- Kahn - Power Rule (integer exponent)

**4) Product & Quotient Rule**

**5) Review**

- Review notes on the quotient rule | Annotated
- Derivatives using Power, Product and Quotient Rules WS | Answers

**6) Product and Quotient Rule with Symbolic Notation**

- Explanation:
- Practice Problems

**7) Derivative of Trig Ratios**

**8) Chain Rule**

**9) Chain Rule (advanced)**

- Explanation
- Practice Problems

**10) Derivative of Exponential & Logarithmic Expressions**

- Explanation:
- Practice Problems:
- Exponential and Log Derivatives Worksheet #1 | Answers
- Exponential and Log Derivatives Worksheet #2 | Answers
- Khan Practice:
- Chain Rule 1
- Review Product Rule
- Quotient Rule
- Special Derivatives (includes power rule, ln(x), e^x and trig ratios)

**11) Use differentiation rules when given the definition of a derivative Worksheet | Answers**

**12) Derivative Rules using tables and graphs **

**13) Review Summary: **

**The Chain Rule.**The last operator is what you keep; all of the other operators are "u."- When should you use the chain rule:
- When you have a power (numerical exponent) and the base is anything other than a single variable.
- When you have a trig ratio and the "inside" part is anything other than a single variable
- When you have an exponential function (the base is a number) and the exponent is anything other than a single variable.
- When you have a logarithmic function and the "inside" part is anything other than a single variable.

- Chain Rule Mixed Review WS | Answers

**14) Derivative at a point with a calculator **

**15) Implicit differentiation - one dy/dx**

- Explanation:
- Practice Problems:

**16) Implicit differentiation - more than one dy/dx**

**17) Review Implicit Differentiation**

- Practice Problems
- Worksheet | Answers
- 2008 Form B Q6
- 2005 (Form B) Q5
- 2004 Q4 - parts a and b
- 2000 Q5
- 1998 Q6

**18) Derivative of Inverse Functions**

- Explanation:
- Practice Problems:
- Derivative of Inverse Functions WS | Answers
- 2007 Q3 - parts a and d

**19) Derivative of Inverse Functions with the graphing calculators**

- Explanation

**20) Derivative of Inverse Trig Ratios**

- Explanation:
- Practice Problems:

**21) Points of Non-Differentiability**

- Explanation:
- Notes | Annotated
- Video: Hollis: The derivative (slide #9)

- Practice Problems:

**22) Review: **

- Derivative Review WS | Answers
- Derivative Word Problem Project
- 2012 Q4 - parts a, b, c
- 2007 Q3 - parts a and b
- 2006 Q6
- 2003 (Form B) Q1 - part a
- 2003 Q6 - parts a and c
- 2001 Q2 - parts a and c
- 2001 Q5 - part a