Derivatives of Exponential and Trigonometric Functions
Students extend their differentiation techniques to include exponential and sinusoidal functions. They apply these new derivatives to model periodic and exponential phenomena.
About This Topic
Students extend their differentiation techniques to include exponential and sinusoidal functions. They apply these new derivatives to model periodic and exponential phenomena.
Key Questions
- What is the derivative of the natural exponential function?
- How do the derivatives of sine and cosine relate to their graphs?
- How do we apply the chain rule to trigonometric functions?
Active Learning Ideas
See all activities→Activities & Teaching Strategies
See all activities
Planning templates for Calculus and Vectors
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 Derivatives and Their Applications
Rules of Differentiation
Students develop and apply the power, product, quotient, and chain rules for differentiating polynomial and rational functions. They extend these rules to composite functions.
8 methodologies
Curve Sketching
Students use first and second derivatives to determine intervals of increase and decrease, local extrema, concavity, and points of inflection. They combine this with asymptotic behaviour to sketch accurate graphs.
8 methodologies
Optimization and Related Rates
Students apply calculus to solve real-world optimization problems and related rates scenarios. They translate physical situations into mathematical models to find maximums, minimums, and rates of change.
8 methodologies