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Choose an age or grade in step 2. Start easier if the pupil is unsure – you can switch anytime and get new problems instantly.

Can I see the problems before printing?

Yes. The sheet shows exactly the problems that will print. Click New problems to swap them.

How do I include an answer key?

Turn on Answer key in the last step. It prints on its own page after the problems, with the same numbering.

What does the question mark next to a problem do?

It opens a step-by-step explanation of the method on screen. It is not printed and does not reveal the answer.

Grade 12Common Core (CCSS) · Math: algebra

Math · Grade 12Derivative Worksheets — Free High School Printables with Answers

Practise the power rule: differentiate polynomials and evaluate f′ at a point.

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Classroom · 10 questions per page

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Derivatives of polynomials · Grade 12

Name: ____________________

Worked example

Differentiate term by term: axⁿ becomes n·a·xⁿ⁻¹, constants become 0.
Put the x-value into f′(x).
Example: f(x) = x³ + 2x gives f′(x) = 3x² + 2, so f′(1) = 5.

Example: how to solve it

Find f′(1): f(x) = 3x² − 8x − 1

Find f′(-2): f(x) = −4x² − 6x − 6

Find f′(1): f(x) = 4x² + 8x − 2

Find f′(1): f(x) = −3x² + 3x − 1

Find f′(-1): f(x) = −2x² − 9x − 4

Find f′(2): f(x) = −x² − 6

Find f′(4): f(x) = 3x² − 7x + 5

Find f′(2): f(x) = 5x² − 4x − 7

Find f′(0): f(x) = −2x² + 3x − 9

10.

Find f′(2): f(x) = −3x² + 6x − 5

11.

Find f′(4): f(x) = −x² − x + 9

12.

Find f′(4): f(x) = 2x² + x − 3

13.

Find f′(-2): f(x) = −5x² + 7

14.

Find f′(-3): f(x) = −4x² + x − 3

15.

Find f′(3): f(x) = x² − 4

16.

Find f′(4): f(x) = x² − 2x − 4

17.

Find f′(-2): f(x) = −x² + 8x − 5

18.

Find f′(1): f(x) = −3x² − 9x + 5

19.

Find f′(1): f(x) = −3x² + 7x + 9

20.

Find f′(1): f(x) = x² + 8x + 9

Answer key

1. -2
2. 10
3. 16
4. -3
5. -5
6. -4
7. 17
8. 16
9. 3
10. -6
11. -9
12. 17
13. 20
14. 25
15. 6
16. 6
17. 12
18. -15
19. 1
20. 10

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Area: Algebra
Exercise type: Derivatives of polynomials
Grade: 12 (ages 17–18)
Difficulty: Easy
Number of tasks: 20
Task format: Calculations
Paper size: US Letter

1. Choose content

Area

Your choices

Area: Algebra
Exercise type: Derivatives of polynomials
Grade: 12 (ages 17–18)
Difficulty: Easy
Number of tasks: 20
Task format: Calculations
Paper size: US Letter

1. Choose content

Area

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Practise the power rule: differentiate polynomials and evaluate f′ at a point.

How to use the tool

Pick difficulty and number of tasks.
Print or save as PDF with the answer key.
“Create new version” gives new numbers.

About this generator

The derivative of xⁿ is n·xⁿ⁻¹. Easy uses quadratics, medium and hard use cubics. The answer key is calculated by the website. No sign-up needed.

Popular uses

Homework
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Lesson starters

Frequently asked questions

How do I pick the right level?: Choose an age or grade in step 2. Start easier if the pupil is unsure – you can switch anytime and get new problems instantly.
Can I see the problems before printing?: Yes. The sheet shows exactly the problems that will print. Click New problems to swap them.
How do I include an answer key?: Turn on Answer key in the last step. It prints on its own page after the problems, with the same numbering.
What does the question mark next to a problem do?: It opens a step-by-step explanation of the method on screen. It is not printed and does not reveal the answer.
Which grade are these for?: Typically grade 12 / calculus.