DIFFERENTIATION Definition of the Derivative and the Tangent Line Problem; Differentiability o Tangent Line Introduction to the definition of the derivative More on the definition of the derivative Definition of the derivative at a point Definition of the derivative Even more on the definition of the derivative Definition of Derivative applet Another definition of derivative applet Algebraic definition of the derivative Problems, solutions, and explanations on the definition of the derivative Slopes, Tangents, and Derivatives o Difference Quotient (slide show) Derivative at a point applet o Tabular view of the derivative o Relationship of the graph of f and f ' Graphing the derivative -- good problems under Exercises for this Topic o o o o o o o Second derivative applet A tabular view of the second derivative Twice differentiable function applet Geometric interpretation of the derivative The derivative illustrated by a surfer A function and its derivative plotter Animated view of a secant line approaching a tangent line Animated View of zooming in on a tangent line -linearization of a curve Secant line approaching a tangent line applet Secant and Tangent line animation for y = x3, y = x sin (1/x), and y = x2 sin (1/x) Secants approaching tangent demonstration Secant and tangent lines plotter Average rate of change and the derivative Average rate of change Instantaneous rates of change Instantaneous rate of change applet Rates of change problems, solutions, and explanations One-sided derivatives applet Derivative drawn from slopes demonstration Derivative Calculator applet Graphs the Derivative with the function applet The derivative as a function: algebraic approach The derivative function applet o Differentiability implies Continuity Theorem A continuous nowhere differentiable function Another nowhere differentiable function applet Continuity and differentiability Problems on the importance of differentiation Finding derivatives numerically on your calculator (instructions) o Differentiability and what it means o Making a piecewise function continuous and differentiable Differentiation Rules: Power Rule, Product Rule, & Quotient Rule o Power Rule Some differentiation rules More on Differentiation Rules Proof of the power rule Derivative of a cubic applet Constant. line, and power functions applet Constant multiple applet Combination: sum, and difference applet Power Rule (slide show) Problems to work o Product Rule Rules to use in calculating derivatives of functions Differentiation using the product rule Applet illustrating and explaining the Product Rule Product Rule (slide show) Drill problems o Quotient Rule Differentiation using the quotient rule Product and Quotient rules Product and Quotient rules problems, solutions, and explanations Proof of the quotient rule Quotient Rule (slide show) Product and Quotient rule applet o Position, velocity, acceleration More on velocity, acceleration, & other rates of change Average Rates of Change The derivative as a rate of change: numerical approach Animated bouncing ball and problem Moving Man applet o o Motion on a line applet Instructions for using your calculator to simulate particle motion problem Review Problems on displacement -- Go to Calculus Book I, then Applications of the Derivative, then Rate of Change, then Displacement Problems to work Differentiation Rules for Trigonometric Functions o Derivative of sin x applet o More on derivatives of trigonometric functions -- good problems under Section 3 Exercises Finding derivatives of trigonometric functions Formulas for derivatives of trigonometric functions Derivatives of Trigonometric Functions Derivatives of Trigonometric Functions problems, solutions, and explanations o Trigonometric functions derivatives applet o Proof that p is irrational Chain Rule o More on the chain rule Chain Rule (slide show) More on the chain rule Chain rule applet o Differentiation using the chain rule Chain rule applet Using the chain rule Chain Rule problems, solutions, and explanations o Problems--decomposing a composed function o Proof of the chain rule o Graphical Differentiation Worksheet o Transformations of functions and derivatives applet Implicit Differentiation o Implicit differentiation Even more on implicit differentiation o Graph a sine function of your choosing o Graph derivative with implicit function applet Implicit function plotter o Problems to work More problems to work Implicit Differentiation problems, solutions, and explanations Related Rates o Related Rates Explained Related Rates problems, solutions, and explanations o Balloon Problem Melting snowball problem applet o Related Rates Animation, three problems, video explanation, & exercises Related Rates airplane problem demonstration o Find the error o Review problems on related rates--Go to Calculus Book I, then Applications of the Derivative, then Related Rates Related Rates problems Related Rates - solve the Turvey by doing the problems Related Rates problems & solutions More Related Rates problems & solutions Summaries and Review Problems: Derivative Rules through Chain Rule o Find the error o Summary of introduction to the derivative A list of differentiation formulas Techniques of Differentiation summary o Proofs of Various Derivative Formulas o Interpretation of the Derivative problems, solutions, and explanations (rates of change) Differentiation Formulas problems, solutions, and explanations o Review problems for finding the slope and equation of a tangent line -- Go to Calculus Book I, then Derivatives, then Slope and Tangents, then Tangent Line Slope or Tangent Line Equation Review problems for linearizing a function--Go to Calculus Book I, then Derivatives, then Linearization, then Linearization again Review problems for finding derivatives with the above methods -- Go to Calculus Book I, then Techniques and Theory of Differentiation, then anything in sections 1 through 4 Review problems on velocity -- Go to Calculus Book I, then Applications of the Derivative, then Rate of Change, then Velocity o o o Problems involving trigonometric functions Lots of differentiation problems to do More problems to do More derivative problems Introduction to derivative problems Quiz on differentiating functions Review quiz for related rates problems (do quiz 327 and quiz 341)