Standard D04: Finding Derivatives Using Chain Rule
Standard D04 Overview:
| standard_d04.pdf |
| standard_d04.docx |
Objectives & Resources:
1. Understand that the derivative of a function is defined as the limit of a difference quotient and can be determined using a variety of strategies, including the "Chain Rule." [EU2.1]
2. Know that the Chain Rule provides a way to differentiate functions created by "composing" other functions. These "composed functions" can also be called "composite functions." [EK 2.1C4]
1. Understand that the derivative of a function is defined as the limit of a difference quotient and can be determined using a variety of strategies, including the "Chain Rule." [EU2.1]
2. Know that the Chain Rule provides a way to differentiate functions created by "composing" other functions. These "composed functions" can also be called "composite functions." [EK 2.1C4]
- Desmos Activity: Exploring the Derivative of Composite Functions
- Khan Academy: Chain rule introduction
- Khan Academy: Practice: Identify composite functions
- (optional) Discovering the chain rule graphically (Sheldon P. Gordon's teacher's guide that inspired the Desmos Activity above)
| gordon_discovering-chain-rule.pdf |
3. Understand why the Chain Rule works the way it does.
- Textbook 3.4, page 151: Intuition behind the chain rule
- Textbook 3.4, page 151: The Chain Rule (Leibniz Notation)
- Textbook 3.4, page 152: The Chain Rule (Lagrange Notation)
4. Be able to calculate derivatives using the Chain Rule. [LO 2.1C]
- Khan Academy: Worked example: Derivative of cos³(x) using the chain rule
- Khan Academy has several other worked out example videos! (not listed here)
- Khan Academy: Practice: Chain rule intro
- Khan Academy: Practice: Chain rule with tables
- Khan Academy: Practice: Chain rule capstone
- Sample Assessment Items: Textbook Exercises 3.4 (pages 155-157) 1-29 ODD, 35, 39, 43, 57, 59, 61, 63, 67, 71, 73. (See solutions under Husky Hub Topics.)
- Sample Assessment Items: Textbook Exercises 3.5 (pages 162-164) 5, 7, 11, 13, 15, 17, 19, 21, 23, 25, 27, 43, 45, 49, 59, 65.