Differentiation
Lesson 2 of 11
Chain, product and quotient rules
Objective. Differentiate composite, product and quotient functions.
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
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Forgetting the inner derivative in the chain rule.
Your progress
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