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Chain Rule - Worksheet 4 - 12th Grade

Medium

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

medium: Practice the same exercise types with a fresh numbered set.

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

About This Worksheet

This medium-level worksheet contains 22 problems designed for 12th Grade students practicing chain rule. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

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:
  1. Differentiate the outer power.
  2. 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.
1
Differentiate with respect to x: f(x) = (2·x+6)^4.
2
Differentiate with respect to x: f(x) = (1·x+6)^2.
3
Differentiate with respect to x: f(x) = (5·x+8)^4.
4
Differentiate with respect to x: f(x) = (5·x+7)^5.
5
Differentiate with respect to x: f(x) = (3·x+4)^4.
6
Differentiate with respect to x: f(x) = (3·x+8)^2.
7
Differentiate with respect to x: f(x) = (4·x+1)^3.
8
Differentiate with respect to x: f(x) = (6·x+6)^4.
9
Differentiate with respect to x: f(x) = (2·x+8)^4.
10
Differentiate with respect to x: f(x) = (1·x+5)^4.
11
Differentiate with respect to x: f(x) = (2·x+6)^5.
12
Differentiate with respect to x: f(x) = (4·x+2)^4.
13
Differentiate with respect to x: f(x) = (4·x+9)^5.
14
Differentiate with respect to x: f(x) = (3·x+7)^3.
15
Differentiate with respect to x: f(x) = (7·x+1)^2.
16
Differentiate with respect to x: f(x) = (7·x+9)^2.
17
Differentiate with respect to x: f(x) = (3·x+8)^3.
18
Differentiate with respect to x: f(x) = (6·x+9)^4.
19
Differentiate with respect to x: f(x) = (7·x+7)^5.
20
Differentiate with respect to x: f(x) = (8·x+8)^5.
21
Differentiate with respect to x: f(x) = (5·x+4)^2.
22
Differentiate with respect to x: f(x) = (5·x+3)^4.

Answer Key

1. f′(x) = 8·(2·x+6)^32. f′(x) = 2·(1·x+6)^13. f′(x) = 20·(5·x+8)^34. f′(x) = 25·(5·x+7)^45. f′(x) = 12·(3·x+4)^36. f′(x) = 6·(3·x+8)^17. f′(x) = 12·(4·x+1)^28. f′(x) = 24·(6·x+6)^39. f′(x) = 8·(2·x+8)^310. f′(x) = 4·(1·x+5)^311. f′(x) = 10·(2·x+6)^412. f′(x) = 16·(4·x+2)^313. f′(x) = 20·(4·x+9)^414. f′(x) = 9·(3·x+7)^215. f′(x) = 14·(7·x+1)^116. f′(x) = 14·(7·x+9)^117. f′(x) = 9·(3·x+8)^218. f′(x) = 24·(6·x+9)^319. f′(x) = 35·(7·x+7)^420. f′(x) = 40·(8·x+8)^421. f′(x) = 10·(5·x+4)^122. f′(x) = 20·(5·x+3)^3

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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 22 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.