DIFFERENTIATION
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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
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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
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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
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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
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Velocity
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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)