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