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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.

Differentiate y = (3x² + 1)⁵
Coordinate grid with the line Differentiate y = (3x² + 1)⁵
  1. 1Outer derivative: 5(3x² + 1)⁴.
  2. 2Inner derivative: 6x.
  3. 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.

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