Introduction to Derivatives
Students define the derivative using the limit definition and interpret it as an instantaneous rate of change and slope of the tangent.
About This Topic
Students define the derivative using the limit definition and interpret it as an instantaneous rate of change and slope of the tangent.
Key Questions
- Analyze the relationship between the secant line and the tangent line in the context of derivatives.
- Justify why the derivative of a function is also a function itself.
- Compare the average rate of change with the instantaneous rate of change.
Active Learning Ideas
See all activities→Activities & Teaching Strategies
See all activities
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Calculus: The Study of Change
Introduction to Limits
Students explore the intuitive concept of a limit by examining function behavior as input values approach a specific point.
8 methodologies
Formal Definition of Limits and Continuity
Students analyze the formal epsilon-delta definition of a limit and apply it to determine function continuity.
8 methodologies
Basic Differentiation Rules
Students apply power, constant multiple, sum, and difference rules to differentiate polynomial functions efficiently.
8 methodologies
Product and Quotient Rules
Students apply the product and quotient rules to differentiate functions involving multiplication and division.
8 methodologies
The Chain Rule
Students apply the chain rule to differentiate composite functions, understanding its role in nested functions.
8 methodologies
Implicit Differentiation
Students learn to differentiate equations where y is not explicitly defined as a function of x, using implicit differentiation.
8 methodologies