Derivatives of Parametric Equations
12th GradeMath45 min
Learning Objective
I can calculate the first and second derivatives of a parametric equation.
Lesson Flow
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Guided Notes
Key concepts students will learn:
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The first derivative of parametric equations requires applying the chain rule, finding dydt and dxdt, and then dividing dydt by dxdt.
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To find the second derivative, determine the derivative of the first derivative with respect to T and divide that by dxdt.
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The curve is concave up when the second derivative is positive and concave down when the second derivative is negative.
Practice
10 questions • Multiple choice & Short answer
Exit Ticket
“Given the parametric equations x = 3cos(2t)sin(t) and y = 3sin²(t)cos(t), find the second derivative d²y/dx² at t = π/4. Show all steps.”
Teacher Guide
Get the complete package:
- Answer keys for all questions
- Differentiation strategies
- Extension activities
- Printable student handouts
