Calculus‎ > ‎

### Derivatives

 Flash Cards1) Average Rate of ChangeExplanation:Notes | AnnotatedVideo: 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 = 0PracticeWorksheet | Answers2) Definition of a Derivative Explanation:Notes | AnnotatedVideos: Kahn: Calculus: Derivatives 1 (new HD version) - general definitionKahn: Calculus: Derivatives 2.5 (new HD version) - find the derivative using the definitionHollis:  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 changesTangent 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 functionPractice Problems:Worksheet | Answers3) Power Rule (and sum/difference, and constant multiple rules)Explanation:Notes | AnnotatedKhan video: Calculus: Derivatives 3: Determining the derivatives of simple polynomials.Practice: Worksheet | AnswersKahn - Power Rule (integer exponent)4) Product & Quotient RuleExplanation:Notes | AnnotatedPractice Problems:Worksheet | Answers5)  Review6) Product and Quotient Rule with Symbolic NotationExplanation:Notes | AnnotatedPractice Problems7) Derivative of Trig RatiosExplanation: Notes | AnnotatedPractice Problems:Worksheet | Answers8) Chain RuleExplanation:Notes | AnnotatedPractice Problems:Worksheet | Answers9) Chain Rule (advanced)ExplanationNotes | AnnotatedPractice Problems 10)  Derivative of Exponential & Logarithmic Expressions Explanation: Notes | AnnotatedKahn videos: Equation of a Tangent linePractice Problems:Exponential and Log Derivatives Worksheet #1 | AnswersExponential and Log Derivatives Worksheet #2 | AnswersKhan Practice: Chain Rule 1 Review Product RuleQuotient RuleSpecial Derivatives (includes power rule, ln(x), e^x and trig ratios)11)  Use differentiation rules when given the definition of a derivative Worksheet | Answers12)  Derivative Rules using tables and graphs Practice Problems Worksheet | Answers13) 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  |  Answers14)  Derivative at a point with a calculator  15) Implicit differentiation - one dy/dxExplanation:Practice Problems:Worksheet | Answers16)  Implicit differentiation - more than one dy/dxExplanationNotes | AnnotatedPractice Problems Worksheet | Answers17) Review Implicit DifferentiationPractice ProblemsWorksheet | Answers2008 Form B Q62005 (Form B) Q52004 Q4 - parts a and b2000 Q5 1998 Q6 18)  Derivative of Inverse FunctionsExplanation:Notes | AnnotatedPractice Problems:Derivative of Inverse Functions WS | Answers2007 Q3 - parts a and d19) Derivative of Inverse Functions with the graphing calculatorsExplanationNotes20)  Derivative of Inverse Trig RatiosExplanation:Notes | AnnotatedPractice Problems:Inverse Trig Derivatives and Inverse Function Derivatives WS  | Answers21) Points of Non-DifferentiabilityExplanation:Notes | AnnotatedVideo: Hollis: The derivative (slide #9)Practice Problems:Continuous and Differentiable WS | Answers22) Review: Derivative Review WS | AnswersDerivative Word Problem Project2012 Q4 - parts a, b, c2007 Q3 - parts a and b2006 Q62003 (Form B) Q1 - part a2003 Q6 - parts a and c2001 Q2 - parts a and c2001 Q5 - part a23)  Derivative Cumulative WS | Answers