Chain Rule Worksheet 1 | 12th Grade Easy

Differentiate functions exactly, state necessary domains and check the resulting symbolic expression.

easy: Start with the preview and follow the worked example.

18 problems · 25-30 minutes · Skills: derivatives, chain rule, calculus

About This Worksheet

This easy-level worksheet contains 18 problems designed for 12th Grade students practicing chain rule. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.

Manipulate algebraic expressions and understand functions, limits and derivative notation.

Differentiate functions exactly, state necessary domains and check the resulting symbolic expression.
Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Differentiate with respect to x: f(x) = (4·x+7)^3.

Solution Steps:

Differentiate the outer power.
Multiply by the derivative of the inner linear expression.

Answer: f′(x) = 12·(4·x+7)^2

Tip: Check your result using the method in the example before moving to the next question.

Paper Include separate answer key in PDF

Differentiate with respect to x: f(x) = (2·x+4)^4.

Differentiate with respect to x: f(x) = (1·x+4)^5.

Differentiate with respect to x: f(x) = (1·x+6)^3.

Differentiate with respect to x: f(x) = (5·x+8)^2.

Differentiate with respect to x: f(x) = (7·x+3)^4.

Differentiate with respect to x: f(x) = (2·x+1)^2.

Differentiate with respect to x: f(x) = (2·x+7)^4.

Differentiate with respect to x: f(x) = (3·x+7)^5.

Differentiate with respect to x: f(x) = (3·x+9)^3.

Differentiate with respect to x: f(x) = (4·x+9)^5.

Differentiate with respect to x: f(x) = (8·x+9)^2.

Differentiate with respect to x: f(x) = (6·x+2)^3.

Differentiate with respect to x: f(x) = (5·x+8)^3.

Differentiate with respect to x: f(x) = (8·x+3)^5.

Differentiate with respect to x: f(x) = (4·x+1)^3.

Differentiate with respect to x: f(x) = (7·x+4)^2.

Differentiate with respect to x: f(x) = (7·x+9)^2.

Differentiate with respect to x: f(x) = (8·x+8)^3.

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)^17. f′(x) = 8·(2·x+7)^38. f′(x) = 15·(3·x+7)^49. f′(x) = 9·(3·x+9)^210. f′(x) = 20·(4·x+9)^411. f′(x) = 16·(8·x+9)^112. f′(x) = 18·(6·x+2)^213. f′(x) = 15·(5·x+8)^214. f′(x) = 40·(8·x+3)^415. f′(x) = 12·(4·x+1)^216. f′(x) = 14·(7·x+4)^117. f′(x) = 14·(7·x+9)^118. f′(x) = 24·(8·x+8)^2

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What skills does this derivatives worksheet cover?

This worksheet focuses on derivatives, chain rule, calculus. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 18 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.