Chain, product and quotient rules
Objective. Differentiate composite, product and quotient functions.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Chain rule handles a function inside a function; product and quotient rules handle multiplication and division of functions.
Worked example
Differentiate y = (3x² + 1)⁵.
- 1Outer derivative: 5(3x² + 1)⁴.
- 2Inner derivative: 6x.
- 3Multiply them.
Answer: 30x(3x² + 1)⁴
Concept mastery
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Practice
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Start practisingCommon mistake. Forgetting the inner derivative in the chain rule.
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