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Grade 12 Derivatives: The Power Rule Worksheet with Answers

Grade 12 (US) · Year 13 (UK) · Class 12 (India) · Math

Unit 5: Introduction to CalculusDerivativesAdvanced

Differentiating polynomials with the power rule and finding slopes of tangent lines. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Derivatives: The Power Rule

Grade 12 · Math

Score___ / 12

Name

Class

Date

Learning goal: Derivatives

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Find f'(x) if f(x) = 6x^2 + 9x - 5.

Answer: f'(x) = 12x + 9

RememberCalculus rules

1
f(x) = 5x^3 - 2x^2 + 2x + 6. Find the slope of the tangent line at x = -3.
Show your work
Answer
2
f(x) = 6x^3 + 9x^2 - 5x + 5. Find the slope of the tangent line at x = -3.
Show your work
Answer
3
Find f'(x) if f(x) = 2x^3 + 9x^2 - 5x - 6.
Answer
4
Find f'(x) if f(x) = 5x^3 - 3x - 6.
Answer
5
Find f'(x) if f(x) = 3x^3 - 3x^2 - 2x - 5.
Answer
6
Find f'(x) if f(x) = 6x^3 + 9x^2 + 3x + 5.
Answer
7
f(x) = 4x^3 + 7x^2 + 9x + 5. Find the slope of the tangent line at x = 2.
Show your work
Answer
8
Find f'(x) if f(x) = x^3 - 5x^2 + 5.
Answer
9
f(x) = 6x^3 - 2x^2 - x + 1. Find the slope of the tangent line at x = -2.
Show your work
Answer
10
Find f'(x) if f(x) = 2x^3 - 4x^2 - 2x + 5.
Answer
11
Find f'(x) if f(x) = x^3 + 3x^2 - 8x.
Answer
12
f(x) = 3x^3 + 6x^2 + 5x. Find the slope of the tangent line at x = -3.
Answer

★ Challenge corner for fast finishers

How many ways can a team of 3 be chosen from 7 students?

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/12/derivatives_power

Answer key (click to show)

1.149
2.103
3.f'(x) = 6x^2 + 18x - 5
4.f'(x) = 15x^2 - 3
5.f'(x) = 9x^2 - 6x - 2
6.f'(x) = 18x^2 + 18x + 3
7.85
8.f'(x) = 3x^2 - 10x
9.79
10.f'(x) = 6x^2 - 8x - 2
11.f'(x) = 3x^2 + 6x - 8
12.50
★35 (challenge corner)

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