Chain Rule Worksheets
Differentiate functions exactly, state necessary domains and check the resulting symbolic expression.
Before you begin
Manipulate algebraic expressions and understand functions, limits and derivative notation.
Worked example
Differentiate with respect to x: f(x) = (4·x+7)^3.
- Differentiate the outer power.
- Multiply by the derivative of the inner linear expression.
Answer: f′(x) = 12·(4·x+7)^2
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Differentiate with respect to x: f(x) = (2·x+4)^4.
2
Differentiate with respect to x: f(x) = (1·x+4)^5.
3
Differentiate with respect to x: f(x) = (1·x+6)^3.
4
Differentiate with respect to x: f(x) = (5·x+8)^2.
5
Differentiate with respect to x: f(x) = (7·x+3)^4.
6
Differentiate with respect to x: f(x) = (2·x+1)^2.
Answer Key
1. f′(x) = 8·(2·x+4)^32. f′(x) = 5·(1·x+4)^43. f′(x) = 3·(1·x+6)^24. f′(x) = 10·(5·x+8)^15. f′(x) = 28·(7·x+3)^36. f′(x) = 4·(2·x+1)^1