Calculus · Week 11 · Differentiation: Composite, Implicit, and Inverse Functions
Implicit Differentiation
Finding slopes on curves like circles, and noticing where my own mistakes tend to happen.
- Students will
- Students use implicit differentiation to find dy/dx and the slope at a point on 3 curves.
- SEL skill
- Rate confidence honestly and name the step where your errors tend to happen
- What it looks like
- Students practice self-awareness by rating their confidence and naming the step where their errors tend to happen.
- Content focus
- Implicit differentiation
- Format
- Think write pair share
Self-awareness
Self-awareness means knowing your own thoughts and habits, like noticing how sure you feel and where your mistakes tend to happen. More self-awareness 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 3.2: AP Calculus AB, Unit 3, Topic 3.2
- Standard for Mathematical Practice: MP6 Attend to precision
- CA Mathematics Framework (2023): Exploring Changing Quantities
- Traditional course: Calculus
More self-awareness activities for Calculus
- What Changes, and How Fast? Self-awarenessAverage rate of change on smaller and smaller intervals, and noticing how confident each step feels.
- The Derivative as a Limit Self-awarenessFrom average to instantaneous rate of change, finding the derivative as a limit and noticing which steps feel strong.
- The Mean Value Theorem Self-awarenessChecking conditions before claiming a theorem applies, and knowing how sure you are.
- Accumulation: Area Under a Rate Self-awarenessEstimating total change from a rate table with Riemann and trapezoidal sums, and noticing how sure we feel.
Previous: The Chain Rule · Next: Inverse Functions and Their Derivatives
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.