Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Differentiation: further techniques, higher derivatives, stationary points
Learning Objective/s:
  • Apply product, quotient, chain, implicit, and parametric differentiation rules to compute first and higher‑order derivatives.
  • Derive and use Leibniz’s rule for the nth derivative of a product.
  • Identify stationary points, classify them using the second‑derivative and higher‑order tests, and determine points of inflection.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with differentiation problems
  • Graphing calculator or Desmos access
  • Prepared example slides (product rule, Leibniz rule, stationary‑point classification)
  • Whiteboard markers
 Introduction:
Recall how we used differentiation to find slopes of curves and predict motion. Students should already know the basic product, quotient and chain rules. Today they will extend those ideas to implicit, parametric and higher‑order differentiation and learn to classify stationary points. Success will be measured by accurate calculations and correct classifications in the exit ticket.
Lesson Structure:
  1. Do‑now (5'): Quick mental quiz on product, quotient and chain rules; teacher reviews answers.
  2. Mini‑lecture (10'): Review advanced techniques (implicit, parametric, inverse differentiation) with worked examples.
  3. Guided practice (15'): Paired activity applying Leibniz’s rule to a product; complete worksheet segment.
  4. Higher‑order derivatives activity (10'): Derive successive derivatives of \(e^{3x}\sin2x\) and discuss patterns.
  5. Stationary‑point investigation (15'): Solve \(f'(x)=0\) for a polynomial, use the second‑derivative test and, if needed, higher‑order tests to classify the point.
  6. Exit ticket (5'): Write one correctly classified stationary point and one formula for an nth‑order derivative.
Conclusion:
We recap the new differentiation techniques, the use of Leibniz’s rule, and the systematic approach to classifying stationary points. Students submit their exit tickets, demonstrating mastery of today’s objectives. For homework, complete the worksheet on implicit and parametric differentiation and solve additional stationary‑point problems from the textbook.