Lesson Plan

• Apply the product rule to differentiate the product of two functions.
• Apply the quotient rule to differentiate the quotient of two functions.
• Identify appropriate u and v (and numerator/denominator) and simplify the resulting expression.
• Extend the product rule to three or more factors by repeated application.
• Solve exam‑style problems efficiently while checking domain restrictions.

• Projector or interactive whiteboard
• Printed worksheet with product/quotient rule problems
• Scientific calculators
• Formula cards (product rule, quotient rule, common derivatives)
• Graphing software/Desmos for visual illustration

Begin with a quick real‑world example (e.g., speed = distance ÷ time) to show why differentiating quotients matters. Review the concept of a derivative as an instantaneous rate of change. State that by the end of the lesson students will be able to correctly apply the product and quotient rules and check their work against the success criteria.

1. Do‑Now (5'): Simple derivative recall on the board; students write the power, trig, exponential rules.
2. Mini‑lecture (10'): Derive the product rule step‑by‑step, emphasising the “differentiate first, keep second, then add” wording.
3. Guided practice (12'): Work through Example 1 together, prompting students to identify u and v and fill a formula card.
4. Extension (8'): Demonstrate the three‑factor product example, showing repeated use of the rule.
5. Quotient rule derivation (8'): Quick algebraic proof, followed by a check‑for‑understanding question.
6. Partner activity (15'): Students solve Example 3 and Example 4 on worksheets, then swap to peer‑check.
7. Whole‑class summary (5'): Highlight common errors (signs, denominator squared) and exam tips.

Recap the two rules, the importance of writing u and v first, and the need to simplify results. Exit ticket: write one product‑rule and one quotient‑rule problem with its answer. Assign homework – a set of mixed differentiation problems requiring both rules and simplification.