Calculus · Week 13 · Differentiation: Composite, Implicit, and Inverse Functions
Choosing the Right Rule
Reading how a function is built before choosing a derivative rule.
- Students will
- Students choose the product, quotient, or chain rule for 4 functions, find each derivative, and find 1 second derivative.
- SEL skill
- Name a function's structure and give a reason before choosing a derivative rule
- What it looks like
- Students practice responsible decision-making by naming the structure of a function and giving a reason before they choose a rule.
- Content focus
- Selecting derivative rules and finding second derivatives
- Format
- Card talk
Responsible decision-making
Responsible decision-making means making choices on purpose, by looking at the facts and having a reason you can explain, like picking a derivative rule after you study the function. 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 3.5: AP Calculus AB, Unit 3, Topic 3.5
- AB 3.6: AP Calculus AB, Unit 3, Topic 3.6
- Standard for Mathematical Practice: MP7 Look for and make use of structure
- 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.
- Inverse Functions and Their Derivatives Responsible decision-makingChoosing between the inverse derivative rule and inverse trig formulas, and explaining the choice.
- 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: Inverse Functions and Their Derivatives · Next: Motion: Position, Velocity, Acceleration
RoseThread Connect activities are drafted with the help of AI and shaped by educators. Students never have to share anything personal. Our five SEL skills are informed by CASEL's SEL Framework; RoseThread Learning is not affiliated with or endorsed by CASEL. AP and Advanced Placement are trademarks of the College Board, which was not involved in making and does not endorse RoseThread Connect.