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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) = 4x^4, find f′(7).

    4 · 4 · 7 · Power-rule differentiation

  2. 2. For f(x) = 11x^5, find f′(6).

    11 · 5 · 6 · Power-rule differentiation

  3. 3. For f(x) = 5x^5, find f′(6).

    5 · 5 · 6 · Power-rule differentiation

  4. 4. For f(x) = 8x^4, find f′(8).

    8 · 4 · 8 · Power-rule differentiation

  5. 5. For f(x) = 9x^2, find f′(5).

    9 · 2 · 5 · Power-rule differentiation

  6. 6. For f(x) = 3x^6, find f′(8).

    3 · 6 · 8 · Power-rule differentiation

  7. 7. For f(x) = 2x^3, find f′(1).

    2 · 3 · 1 · Power-rule differentiation

  8. 8. For f(x) = 3x^2, find f′(5).

    3 · 2 · 5 · Power-rule differentiation

  9. 9. For f(x) = 3x^5, find f′(6).

    3 · 5 · 6 · Power-rule differentiation

  10. 10. For f(x) = 8x^3, find f′(1).

    8 · 3 · 1 · Power-rule differentiation

  11. 11. For f(x) = 4x^3, find f′(7).

    4 · 3 · 7 · Power-rule differentiation

  12. 12. For f(x) = 1x^5, find f′(1).

    1 · 5 · 1 · Power-rule differentiation
12 questions · Seed 53 · 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) = 4x^4, find f′(7).

    5488

    The power rule gives f′(x) = 16x^3. At x = 7, f′(7) = 5488.

  2. 2. For f(x) = 11x^5, find f′(6).

    71280

    The power rule gives f′(x) = 55x^4. At x = 6, f′(6) = 71280.

  3. 3. For f(x) = 5x^5, find f′(6).

    32400

    The power rule gives f′(x) = 25x^4. At x = 6, f′(6) = 32400.

  4. 4. For f(x) = 8x^4, find f′(8).

    16384

    The power rule gives f′(x) = 32x^3. At x = 8, f′(8) = 16384.

  5. 5. For f(x) = 9x^2, find f′(5).

    90

    The power rule gives f′(x) = 18x^1. At x = 5, f′(5) = 90.

  6. 6. For f(x) = 3x^6, find f′(8).

    589824

    The power rule gives f′(x) = 18x^5. At x = 8, f′(8) = 589824.

  7. 7. For f(x) = 2x^3, find f′(1).

    6

    The power rule gives f′(x) = 6x^2. At x = 1, f′(1) = 6.

  8. 8. For f(x) = 3x^2, find f′(5).

    30

    The power rule gives f′(x) = 6x^1. At x = 5, f′(5) = 30.

  9. 9. For f(x) = 3x^5, find f′(6).

    19440

    The power rule gives f′(x) = 15x^4. At x = 6, f′(6) = 19440.

  10. 10. For f(x) = 8x^3, find f′(1).

    24

    The power rule gives f′(x) = 24x^2. At x = 1, f′(1) = 24.

  11. 11. For f(x) = 4x^3, find f′(7).

    588

    The power rule gives f′(x) = 12x^2. At x = 7, f′(7) = 588.

  12. 12. For f(x) = 1x^5, find f′(1).

    5

    The power rule gives f′(x) = 5x^4. At x = 1, f′(1) = 5.

12 questions · Seed 53 · 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) = 4x^4, find f′(7).

    4 · 4 · 7 · Power-rule differentiation

  2. 2. For f(x) = 11x^5, find f′(6).

    11 · 5 · 6 · Power-rule differentiation

  3. 3. For f(x) = 5x^5, find f′(6).

    5 · 5 · 6 · Power-rule differentiation

  4. 4. For f(x) = 8x^4, find f′(8).

    8 · 4 · 8 · Power-rule differentiation

  5. 5. For f(x) = 9x^2, find f′(5).

    9 · 2 · 5 · Power-rule differentiation

  6. 6. For f(x) = 3x^6, find f′(8).

    3 · 6 · 8 · Power-rule differentiation

  7. 7. For f(x) = 2x^3, find f′(1).

    2 · 3 · 1 · Power-rule differentiation

  8. 8. For f(x) = 3x^2, find f′(5).

    3 · 2 · 5 · Power-rule differentiation

  9. 9. For f(x) = 3x^5, find f′(6).

    3 · 5 · 6 · Power-rule differentiation

  10. 10. For f(x) = 8x^3, find f′(1).

    8 · 3 · 1 · Power-rule differentiation

  11. 11. For f(x) = 4x^3, find f′(7).

    4 · 3 · 7 · Power-rule differentiation

  12. 12. For f(x) = 1x^5, find f′(1).

    1 · 5 · 1 · Power-rule differentiation
12 questions · Seed 53 · 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) = 4x^4, find f′(7).

    5488

    The power rule gives f′(x) = 16x^3. At x = 7, f′(7) = 5488.

  2. 2. For f(x) = 11x^5, find f′(6).

    71280

    The power rule gives f′(x) = 55x^4. At x = 6, f′(6) = 71280.

  3. 3. For f(x) = 5x^5, find f′(6).

    32400

    The power rule gives f′(x) = 25x^4. At x = 6, f′(6) = 32400.

  4. 4. For f(x) = 8x^4, find f′(8).

    16384

    The power rule gives f′(x) = 32x^3. At x = 8, f′(8) = 16384.

  5. 5. For f(x) = 9x^2, find f′(5).

    90

    The power rule gives f′(x) = 18x^1. At x = 5, f′(5) = 90.

  6. 6. For f(x) = 3x^6, find f′(8).

    589824

    The power rule gives f′(x) = 18x^5. At x = 8, f′(8) = 589824.

  7. 7. For f(x) = 2x^3, find f′(1).

    6

    The power rule gives f′(x) = 6x^2. At x = 1, f′(1) = 6.

  8. 8. For f(x) = 3x^2, find f′(5).

    30

    The power rule gives f′(x) = 6x^1. At x = 5, f′(5) = 30.

  9. 9. For f(x) = 3x^5, find f′(6).

    19440

    The power rule gives f′(x) = 15x^4. At x = 6, f′(6) = 19440.

  10. 10. For f(x) = 8x^3, find f′(1).

    24

    The power rule gives f′(x) = 24x^2. At x = 1, f′(1) = 24.

  11. 11. For f(x) = 4x^3, find f′(7).

    588

    The power rule gives f′(x) = 12x^2. At x = 7, f′(7) = 588.

  12. 12. For f(x) = 1x^5, find f′(1).

    5

    The power rule gives f′(x) = 5x^4. At x = 1, f′(1) = 5.

12 questions · Seed 53 · Age guidance, not curriculum certification