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What is the derivative of a function, how is calculated, and why is it important?
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Student Learning Map
- Topic:Derivatives
- Subject(s):Math
- Days:25
- Grade(s):11, 12
Key Learning:
Calculate teh derivative of functions, and use the derivative to determine the velocity and other applications.
Unit Essential Question(s):
Concept: Derivatives of Polynomial Functions, Differentiability and Rules Concept: Implicit Differentiation, Inverse Trigonometric, and Logarithmic and Exponential Functions Lesson Essential Question(s):What is the usefulness of a derivative? (A)What is the usefulness of a derivative? (ET)How are derivatives calculated? (A)What are "rules" of differentiation and why are they useful? (A)What are "rules" of differentiation and why are they useful? (ET)Lesson Essential Question(s):How is the derivative used to determine the velocity of an object? (A)What are the derivatives of the six basic trigonometric functions? (A)How is the Chain Rule used, and what benefits exist from knowing this rule? (A)How is the Chain Rule used, and what benefits exist from knowing this rule? (ET)
Additional Info:
Calculus textbook Graphing Calculator Powerpoint from the Internet (G.Kelly) TI-Presenter Ancillary material
Resources:
Culminating Activities:
1. Untitled Culminating ActivityStudent Assessment(s):
1. Untitled Student AssessmentAcquisition Lesson(s):
1. What is the usefulness of a derivative?2. How is the derivative used to determine the velocity of an object?3. When and why is implicit differentiation used?4. How are derivatives calculated?5. What are "rules" of differentiation and why are they useful?6. What are the derivatives of the six basic trigonometric functions?7. How is the Chain Rule used, and what benefits exist from knowing this rule?8. What are the derivatives of the inverse trigonometric functions?9. How is the derivative of an exponentiail function calculated?Extended Thinking Lesson(s):
1. What is the usefulness of a derivative?2. When and why is implicit differentiation used?3. What are "rules" of differentiation and why are they useful?4. How is the Chain Rule used, and what benefits exist from knowing this rule?