Calculus · Week 12 · Differentiation: Composite, Implicit, and Inverse Functions
Inverse Functions and Their Derivatives
Choosing between the inverse derivative rule and inverse trig formulas, and explaining the choice.
- Students will
- Students find derivatives of inverse functions at a point and derivatives of inverse trig functions.
- SEL skill
- Choose a method from clues in the problem and explain the reason
- What it looks like
- Students practice responsible decision-making by choosing a method for each problem and giving a reason.
- Content focus
- Derivatives of inverse functions
- Format
- Small group problem-solving
Responsible decision-making
Responsible decision-making means making careful choices based on evidence, like choosing a method for a problem and having a clear reason. More responsible decision-making activities
What you get
A teacher guide with what to say, step by step, plus student pages and a supports page for students with diverse learning needs, including those with IEPs. Print or Project it, or assign it in Google Forms and Google Docs for Google Classroom. Your first 10 activities are free.
Standards
- AB 3.3: AP Calculus AB, Unit 3, Topic 3.3
- AB 3.4: AP Calculus AB, Unit 3, Topic 3.4
- Standard for Mathematical Practice: MP5 Use appropriate tools strategically
- CA Mathematics Framework (2023): Exploring Changing Quantities
- Traditional course: Calculus
More responsible decision-making activities for Calculus
- Continuity and the Intermediate Value Theorem Responsible decision-makingChecking continuity, fixing removable discontinuities, and deciding when the Intermediate Value Theorem applies.
- Choosing the Right Rule Responsible decision-makingReading how a function is built before choosing a derivative rule.
- Close Enough? Local Linear Approximation Responsible decision-makingUsing a tangent line to estimate and deciding whether to trust it.
- Finding Extreme Values Responsible decision-makingCritical points, sign charts, and choosing the right test to find local and absolute extreme values.
Previous: Implicit Differentiation · Next: Choosing the Right Rule
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