Important Terms and Concepts

Learning OutcomesIn this chapter, students will...

Chapter 4 Sections
41 Combination of Two Functios
Objective: On your own or with a study group, explore the derivatives of functions formed by multiplying, dividing, and composing two functions.
Homework: Problems 16 all
Objective: On your own or with a study group, explore the derivatives of functions formed by multiplying, dividing, and composing two functions.
Homework: Problems 16 all
42 Derivative of a Product of Two Functions
Objective: Given a function that is a product of two other functions, find, in one step, an equation for the derivative function.
Aligned Instructional Resources: Khan Academy Video: "Applying the product rule for derivatives"
Homework  Day 1: Q Problems 110, 122 all
Homework  Day 2: Problems 2335 odd
Objective: Given a function that is a product of two other functions, find, in one step, an equation for the derivative function.
Aligned Instructional Resources: Khan Academy Video: "Applying the product rule for derivatives"
Homework  Day 1: Q Problems 110, 122 all
Homework  Day 2: Problems 2335 odd
43 Derivative of a Quotient of Two Functions
Objective: Given a function whose equation contains a quotient of two other functions, find an equation for the derivative function in one step and simplify the answer.
Homework  Day 1: Q Problems 110, Problems 115 odd
Homework  Day 2: Problems 1729 odd, 30, 32
Objective: Given a function whose equation contains a quotient of two other functions, find an equation for the derivative function in one step and simplify the answer.
Homework  Day 1: Q Problems 110, Problems 115 odd
Homework  Day 2: Problems 1729 odd, 30, 32
44 Derivative of the Other Trigonometric Functions
Objective: Given a function whose equation contains any of the six trigonometric functions, find the equation for the derivative function in one step.
Homework  Day 1: Q Problems 110, Problems 121 odd
Homework  Day 2: Problems 2335 odd, 36
Objective: Given a function whose equation contains any of the six trigonometric functions, find the equation for the derivative function in one step.
Homework  Day 1: Q Problems 110, Problems 121 odd
Homework  Day 2: Problems 2335 odd, 36
45 Derivative of Inverse Trigonometric Functions
Objective: Differentiate each of the six inverse trigonometric functions.
Homework  Day 1: Q Problems 110, Problems 125 odd
Objective: Differentiate each of the six inverse trigonometric functions.
Homework  Day 1: Q Problems 110, Problems 125 odd
46 Differentiability and Continuity
Objective: Prove that a differentiable function is continuous, and use this property to prove that certain functions are continuous.
Homework  Day 1: Q Problems 110, Problems 119 odd, Section 45 14, 16
Homework  Day 2: Problems 2133 odd, Section 45 29
Objective: Prove that a differentiable function is continuous, and use this property to prove that certain functions are continuous.
Homework  Day 1: Q Problems 110, Problems 119 odd, Section 45 14, 16
Homework  Day 2: Problems 2133 odd, Section 45 29
47 Derivative of a Parametric Function
Objective: Given equations for x and y in terms of t, find dx/dt, dy/dt and dy/dx.
Homework  Day 1: Q Problems 110, Problems 15 all
Homework  Day 2: Problems 7, 9, 11, 15
Objective: Given equations for x and y in terms of t, find dx/dt, dy/dt and dy/dx.
Homework  Day 1: Q Problems 110, Problems 15 all
Homework  Day 2: Problems 7, 9, 11, 15
48 Graphs and Derivatives of Implicit Relations
Objective: Given the equation for an implicit relation, find the derivative of y with respect x, and show by graph that the answer is reasonable.
Homework  Day 1: Q Problems 110, Problems 112 all
Homework  Day 2: Problems 1327 odd
Objective: Given the equation for an implicit relation, find the derivative of y with respect x, and show by graph that the answer is reasonable.
Homework  Day 1: Q Problems 110, Problems 112 all
Homework  Day 2: Problems 1327 odd
49 Related Rates
Objective: Given a situation in which several quantities vary, predict the rate at which one of them is changing when you know the other, related rates.
Homework  Day 1: Q Problems 110, Problems 13 all
Homework  Day 2: Problems 47 all
Homework  Day 3: Problems 812 all
Objective: Given a situation in which several quantities vary, predict the rate at which one of them is changing when you know the other, related rates.
Homework  Day 1: Q Problems 110, Problems 13 all
Homework  Day 2: Problems 47 all
Homework  Day 3: Problems 812 all