Grade 12 Chain Rule Worksheets
Start with eight focused practice problems, then use the answer key below to check the worksheet.
Practice Worksheet
Grade 12 Chain Rule Practice
Solve each problem. Show your work.
- 1.Differentiate: f(x) = (4x - 1)^6
- 2.Differentiate: f(x) = (3x - 2)^5
- 3.Differentiate: f(x) = (3x - 2)^6
- 4.Differentiate: f(x) = (3x + 4)^7
- 5.Differentiate: f(x) = (2x - 3)^4
- 6.Differentiate: f(x) = (6x + 3)^4
- 7.Differentiate: f(x) = (5x + 2)^6
- 8.Differentiate: f(x) = (3x + 7)^7
Show answer key
- Question 1: f'(x) = 24(4x - 1)^5
- Question 2: f'(x) = 15(3x - 2)^4
- Question 3: f'(x) = 18(3x - 2)^5
- Question 4: f'(x) = 21(3x + 4)^6
- Question 5: f'(x) = 8(2x - 3)^3
- Question 6: f'(x) = 24(6x + 3)^3
- Question 7: f'(x) = 30(5x + 2)^5
- Question 8: f'(x) = 21(3x + 7)^6
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About These Worksheets
Grade 12 students use the chain rule as a core derivative method for composite functions and applied calculus problems.
Chain rule worksheets focus on differentiating composite functions, where one function is nested inside another. Grade 12 students use the chain rule for expressions such as (3x + 2)^5, square roots of polynomials, and trigonometric or exponential composites when those appear in the course. The core habit is identifying the outside function and the inside function before differentiating.
These worksheets include structured practice with u-substitution notation, increasingly complex composites, and application questions where rates of change depend on linked quantities. Students learn to differentiate the outside while leaving the inside unchanged, then multiply by the derivative of the inside. Chain rule fluency is critical for optimization, related rates, curve sketching, and almost every advanced derivative topic that follows.
Skills Practised
- Identifying inside and outside functions
- Differentiating composite functions
- Using u-substitution notation as an organizer
- Combining chain rule with power rule
- Applying chain rule in rate-of-change contexts
Parent Tip: Chain rule mistakes are usually hidden in the middle step. Use the answer key for the result, and rely on photo checking when your teen needs feedback on the inside/outside function setup.