Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Duration of Days: 15
How can the Chain Rule be used to differentiate composite functions?
What is the relationship between the Chain Rule and the Power Rule?
How can we apply the Chain Rule to functions involving trigonometric, logarithmic, and exponential functions?
What is an implicit function, and how does it differ from an explicit function?
How can we use implicit differentiation to find the derivative of an implicit function?
What are the steps involved in implicit differentiation, and why is it necessary to differentiate both sides of the equation with respect to x?
How can we find the derivative of an inverse function using the Inverse Function Theorem?
3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Selecting Procedures for Calculating Derivatives
3.6 Calculating Higher-Order Derivatives
College Board AP Classroom Assessments
| Lesson # | Lesson Title | Duration of Days |
|---|---|---|
| 1 | 3-1 The Chain Rule | 3 |
| 2 | 3-2 Implicit Differentiation | 3 |
| 3 | 3-3 Differentiating Inverse Functions | 1 |
| 4 | 3-4 Differentiating Inverse Trigonometric Functions | 2 |
| 5 | 3-5 Selecting Procedures for Calculating Derivatives | 2 |
| 6 | 3-6 Calculating Higher-Order Derivatives | 2 |
| 7 | Review and Assessment | 2 |