Derivatives

• 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

  • Worksheet | Answers

• 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:

  • Worksheet | Answers

• Teacher Resources:

  • Desmos Activity: Derivatives and Slope

• Explanation:

  • Notes | Annotated

  • Khan video: Calculus: Derivatives 3: Determining the derivatives of simple polynomials.

• Practice: 

  • Worksheet | Answers

  • Kahn - Power Rule (integer exponent)

• Explanation:

  • Notes | Annotated

• Practice Problems:

  • Worksheet | Answers

• Review notes on the quotient rule | Annotated

• Derivatives using Power, Product and Quotient Rules WS | Answers

• Explanation:

  • Notes | Annotated

• Practice Problems

  • Worksheet | Answers

  • 2003 (Form B) Q1a

• Explanation: 

  • Notes | Annotated

• Practice Problems:

  • Worksheet | Answers

• Explanation:

  • Notes | Annotated

• Practice Problems:

  • Worksheet | Answers

• Explanation

  • Notes | Annotated

• Practice Problems 

  • Worksheet | Answers

  • 2001 Q2 - parts a & c

• Explanation: 

  • Notes | Annotated

  • Kahn videos: 

    • Equation of a Tangent line

• 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)

Worksheet | Answers

• Practice Problems 

  • Worksheet | Answers

• 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

• Notes 

• 2014 Q1 a, b 

• Explanation:

  • Notes | Annotated

  • Khan videos: 

    • Implicit differentiation

    • part 2

    • More implicit differentiation

    • More chain rule and implicit differentiation intuition  

• Practice Problems:

  • Worksheet | Answers

• Explanation

  • Notes | Annotated

• Practice Problems 

  • Worksheet | Answers

• Practice Problems

  • Worksheet | Answers

  • 2008 Form B Q6

  • 2005 (Form B) Q5

  • 2004 Q4 - parts a and b

  • 2000 Q5 

  • 1998 Q6 

• Explanation:

  • Notes | Annotated

• Practice Problems:

  • Derivative of Inverse Functions WS | Answers

  • 2007 Q3 - parts a and d

• Explanation

  • Notes

• Explanation:

  • Notes | Annotated

• Practice Problems:

  • Inverse Trig Derivatives and Inverse Function Derivatives WS  | Answers

• Explanation:

  • Notes | Annotated

  • Video: Hollis: The derivative (slide #9)

• Practice Problems:

  • Continuous and Differentiable WS | Answers

• Derivative Review WS | Answers

• Flash Cards

• 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

Derivative Cumulative WS | Answers