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MathsAges 16-18

Power-rule differentiation

Differentiate a single power term and evaluate its derivative at a specified value of x. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Power-rule differentiation

Take your time. Show your thinking.

  1. 1. For f(x) = 3x^5, find f′(2).

    3 · 5 · 2 · Power-rule differentiation

  2. 2. For f(x) = 7x^3, find f′(4).

    7 · 3 · 4 · Power-rule differentiation

  3. 3. For f(x) = 10x^2, find f′(9).

    10 · 2 · 9 · Power-rule differentiation

  4. 4. For f(x) = 8x^6, find f′(5).

    8 · 6 · 5 · Power-rule differentiation

  5. 5. For f(x) = 12x^2, find f′(6).

    12 · 2 · 6 · Power-rule differentiation

  6. 6. For f(x) = 6x^6, find f′(2).

    6 · 6 · 2 · Power-rule differentiation

  7. 7. For f(x) = 5x^6, find f′(6).

    5 · 6 · 6 · Power-rule differentiation

  8. 8. For f(x) = 10x^2, find f′(7).

    10 · 2 · 7 · Power-rule differentiation

  9. 9. For f(x) = 1x^3, find f′(7).

    1 · 3 · 7 · Power-rule differentiation

  10. 10. For f(x) = 6x^2, find f′(4).

    6 · 2 · 4 · Power-rule differentiation

  11. 11. For f(x) = 2x^5, find f′(7).

    2 · 5 · 7 · Power-rule differentiation

  12. 12. For f(x) = 4x^3, find f′(1).

    4 · 3 · 1 · Power-rule differentiation
12 questions · Seed 46 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Power-rule differentiation

Answers and reasoning. Review before teaching.

  1. 1. For f(x) = 3x^5, find f′(2).

    240

    The power rule gives f′(x) = 15x^4. At x = 2, f′(2) = 240.

  2. 2. For f(x) = 7x^3, find f′(4).

    336

    The power rule gives f′(x) = 21x^2. At x = 4, f′(4) = 336.

  3. 3. For f(x) = 10x^2, find f′(9).

    180

    The power rule gives f′(x) = 20x^1. At x = 9, f′(9) = 180.

  4. 4. For f(x) = 8x^6, find f′(5).

    150000

    The power rule gives f′(x) = 48x^5. At x = 5, f′(5) = 150000.

  5. 5. For f(x) = 12x^2, find f′(6).

    144

    The power rule gives f′(x) = 24x^1. At x = 6, f′(6) = 144.

  6. 6. For f(x) = 6x^6, find f′(2).

    1152

    The power rule gives f′(x) = 36x^5. At x = 2, f′(2) = 1152.

  7. 7. For f(x) = 5x^6, find f′(6).

    233280

    The power rule gives f′(x) = 30x^5. At x = 6, f′(6) = 233280.

  8. 8. For f(x) = 10x^2, find f′(7).

    140

    The power rule gives f′(x) = 20x^1. At x = 7, f′(7) = 140.

  9. 9. For f(x) = 1x^3, find f′(7).

    147

    The power rule gives f′(x) = 3x^2. At x = 7, f′(7) = 147.

  10. 10. For f(x) = 6x^2, find f′(4).

    48

    The power rule gives f′(x) = 12x^1. At x = 4, f′(4) = 48.

  11. 11. For f(x) = 2x^5, find f′(7).

    24010

    The power rule gives f′(x) = 10x^4. At x = 7, f′(7) = 24010.

  12. 12. For f(x) = 4x^3, find f′(1).

    12

    The power rule gives f′(x) = 12x^2. At x = 1, f′(1) = 12.

12 questions · Seed 46 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Power-rule differentiation

Take your time. Show your thinking.

  1. 1. For f(x) = 3x^5, find f′(2).

    3 · 5 · 2 · Power-rule differentiation

  2. 2. For f(x) = 7x^3, find f′(4).

    7 · 3 · 4 · Power-rule differentiation

  3. 3. For f(x) = 10x^2, find f′(9).

    10 · 2 · 9 · Power-rule differentiation

  4. 4. For f(x) = 8x^6, find f′(5).

    8 · 6 · 5 · Power-rule differentiation

  5. 5. For f(x) = 12x^2, find f′(6).

    12 · 2 · 6 · Power-rule differentiation

  6. 6. For f(x) = 6x^6, find f′(2).

    6 · 6 · 2 · Power-rule differentiation

  7. 7. For f(x) = 5x^6, find f′(6).

    5 · 6 · 6 · Power-rule differentiation

  8. 8. For f(x) = 10x^2, find f′(7).

    10 · 2 · 7 · Power-rule differentiation

  9. 9. For f(x) = 1x^3, find f′(7).

    1 · 3 · 7 · Power-rule differentiation

  10. 10. For f(x) = 6x^2, find f′(4).

    6 · 2 · 4 · Power-rule differentiation

  11. 11. For f(x) = 2x^5, find f′(7).

    2 · 5 · 7 · Power-rule differentiation

  12. 12. For f(x) = 4x^3, find f′(1).

    4 · 3 · 1 · Power-rule differentiation
12 questions · Seed 46 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Power-rule differentiation

Answers and reasoning. Review before teaching.

  1. 1. For f(x) = 3x^5, find f′(2).

    240

    The power rule gives f′(x) = 15x^4. At x = 2, f′(2) = 240.

  2. 2. For f(x) = 7x^3, find f′(4).

    336

    The power rule gives f′(x) = 21x^2. At x = 4, f′(4) = 336.

  3. 3. For f(x) = 10x^2, find f′(9).

    180

    The power rule gives f′(x) = 20x^1. At x = 9, f′(9) = 180.

  4. 4. For f(x) = 8x^6, find f′(5).

    150000

    The power rule gives f′(x) = 48x^5. At x = 5, f′(5) = 150000.

  5. 5. For f(x) = 12x^2, find f′(6).

    144

    The power rule gives f′(x) = 24x^1. At x = 6, f′(6) = 144.

  6. 6. For f(x) = 6x^6, find f′(2).

    1152

    The power rule gives f′(x) = 36x^5. At x = 2, f′(2) = 1152.

  7. 7. For f(x) = 5x^6, find f′(6).

    233280

    The power rule gives f′(x) = 30x^5. At x = 6, f′(6) = 233280.

  8. 8. For f(x) = 10x^2, find f′(7).

    140

    The power rule gives f′(x) = 20x^1. At x = 7, f′(7) = 140.

  9. 9. For f(x) = 1x^3, find f′(7).

    147

    The power rule gives f′(x) = 3x^2. At x = 7, f′(7) = 147.

  10. 10. For f(x) = 6x^2, find f′(4).

    48

    The power rule gives f′(x) = 12x^1. At x = 4, f′(4) = 48.

  11. 11. For f(x) = 2x^5, find f′(7).

    24010

    The power rule gives f′(x) = 10x^4. At x = 7, f′(7) = 24010.

  12. 12. For f(x) = 4x^3, find f′(1).

    12

    The power rule gives f′(x) = 12x^2. At x = 1, f′(1) = 12.

12 questions · Seed 46 · Age guidance, not curriculum certification