Differentiation techniques
Lesson 6 of 11
The chain rule
Objective. Differentiate a function of a function.
The key idea
If y = f(g(x)) then dy/dx = f′(g(x)) × g′(x): differentiate the outside, keep the inside, then multiply by the derivative of the inside.
Worked example
Differentiate y = (3x² + 1)⁵.
- 1Outside: 5(3x² + 1)⁴.
- 2Inside derivative: 6x.
- 3Multiply: 30x(3x² + 1)⁴.
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 to multiply by the derivative of the inner function.
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