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Basic Differentiation Rules - Worksheet 5 - 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.

24 problems · 20-25 minutes · Skills: derivatives, differentiation rules, calculus

About This Worksheet

This medium-level worksheet contains 24 problems designed for 12th Grade students practicing basic differentiation rules. 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^3+7·x.
Solution Steps:
  1. Apply the power rule to each term: d(xⁿ)/dx = nx^(n − 1).
Answer: f′(x) = 12·x^2+7
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^2+7·x.
2
Differentiate with respect to x: f(x) = 6·x^3+4·x.
3
Differentiate with respect to x: f(x) = 1·x^2+8·x.
4
Differentiate with respect to x: f(x) = 4·x^2+6·x.
5
Differentiate with respect to x: f(x) = 4·x^5+4·x.
6
Differentiate with respect to x: f(x) = 8·x^5+4·x.
7
Differentiate with respect to x: f(x) = 5·x^5+5·x.
8
Differentiate with respect to x: f(x) = 5·x^3+2·x.
9
Differentiate with respect to x: f(x) = 2·x^5+4·x.
10
Differentiate with respect to x: f(x) = 8·x^3+3·x.
11
Differentiate with respect to x: f(x) = 8·x^3+5·x.
12
Differentiate with respect to x: f(x) = 1·x^2+2·x.
13
Differentiate with respect to x: f(x) = 7·x^2+3·x.
14
Differentiate with respect to x: f(x) = 2·x^2+4·x.
15
Differentiate with respect to x: f(x) = 2·x^4+3·x.
16
Differentiate with respect to x: f(x) = 1·x^5+6·x.
17
Differentiate with respect to x: f(x) = 1·x^2+5·x.
18
Differentiate with respect to x: f(x) = 3·x^5+6·x.
19
Differentiate with respect to x: f(x) = 6·x^2+9·x.
20
Differentiate with respect to x: f(x) = 8·x^5+3·x.
21
Differentiate with respect to x: f(x) = 2·x^2+9·x.
22
Differentiate with respect to x: f(x) = 6·x^4+6·x.
23
Differentiate with respect to x: f(x) = 2·x^5+1·x.
24
Differentiate with respect to x: f(x) = 3·x^4+4·x.

Answer Key

1. f′(x) = 4·x^1+72. f′(x) = 18·x^2+43. f′(x) = 2·x^1+84. f′(x) = 8·x^1+65. f′(x) = 20·x^4+46. f′(x) = 40·x^4+47. f′(x) = 25·x^4+58. f′(x) = 15·x^2+29. f′(x) = 10·x^4+410. f′(x) = 24·x^2+311. f′(x) = 24·x^2+512. f′(x) = 2·x^1+213. f′(x) = 14·x^1+314. f′(x) = 4·x^1+415. f′(x) = 8·x^3+316. f′(x) = 5·x^4+617. f′(x) = 2·x^1+518. f′(x) = 15·x^4+619. f′(x) = 12·x^1+920. f′(x) = 40·x^4+321. f′(x) = 4·x^1+922. f′(x) = 24·x^3+623. f′(x) = 10·x^4+124. f′(x) = 12·x^3+4

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This worksheet focuses on derivatives, differentiation rules, 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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This worksheet contains 24 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.