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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) = 12x^5, find f′(5).

    12 · 5 · 5 · Power-rule differentiation

  2. 2. For f(x) = 5x^6, find f′(4).

    5 · 6 · 4 · Power-rule differentiation

  3. 3. For f(x) = 4x^3, find f′(7).

    4 · 3 · 7 · Power-rule differentiation

  4. 4. For f(x) = 6x^6, find f′(6).

    6 · 6 · 6 · Power-rule differentiation

  5. 5. For f(x) = 1x^2, find f′(5).

    1 · 2 · 5 · Power-rule differentiation

  6. 6. For f(x) = 1x^2, find f′(6).

    1 · 2 · 6 · Power-rule differentiation

  7. 7. For f(x) = 8x^3, find f′(3).

    8 · 3 · 3 · Power-rule differentiation

  8. 8. For f(x) = 12x^6, find f′(5).

    12 · 6 · 5 · Power-rule differentiation

  9. 9. For f(x) = 8x^2, find f′(6).

    8 · 2 · 6 · Power-rule differentiation

  10. 10. For f(x) = 3x^6, find f′(6).

    3 · 6 · 6 · Power-rule differentiation

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

    6 · 4 · 6 · Power-rule differentiation

  12. 12. For f(x) = 5x^3, find f′(1).

    5 · 3 · 1 · Power-rule differentiation
12 questions · Seed 54 · 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) = 12x^5, find f′(5).

    37500

    The power rule gives f′(x) = 60x^4. At x = 5, f′(5) = 37500.

  2. 2. For f(x) = 5x^6, find f′(4).

    30720

    The power rule gives f′(x) = 30x^5. At x = 4, f′(4) = 30720.

  3. 3. For f(x) = 4x^3, find f′(7).

    588

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

  4. 4. For f(x) = 6x^6, find f′(6).

    279936

    The power rule gives f′(x) = 36x^5. At x = 6, f′(6) = 279936.

  5. 5. For f(x) = 1x^2, find f′(5).

    10

    The power rule gives f′(x) = 2x^1. At x = 5, f′(5) = 10.

  6. 6. For f(x) = 1x^2, find f′(6).

    12

    The power rule gives f′(x) = 2x^1. At x = 6, f′(6) = 12.

  7. 7. For f(x) = 8x^3, find f′(3).

    216

    The power rule gives f′(x) = 24x^2. At x = 3, f′(3) = 216.

  8. 8. For f(x) = 12x^6, find f′(5).

    225000

    The power rule gives f′(x) = 72x^5. At x = 5, f′(5) = 225000.

  9. 9. For f(x) = 8x^2, find f′(6).

    96

    The power rule gives f′(x) = 16x^1. At x = 6, f′(6) = 96.

  10. 10. For f(x) = 3x^6, find f′(6).

    139968

    The power rule gives f′(x) = 18x^5. At x = 6, f′(6) = 139968.

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

    5184

    The power rule gives f′(x) = 24x^3. At x = 6, f′(6) = 5184.

  12. 12. For f(x) = 5x^3, find f′(1).

    15

    The power rule gives f′(x) = 15x^2. At x = 1, f′(1) = 15.

12 questions · Seed 54 · 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) = 12x^5, find f′(5).

    12 · 5 · 5 · Power-rule differentiation

  2. 2. For f(x) = 5x^6, find f′(4).

    5 · 6 · 4 · Power-rule differentiation

  3. 3. For f(x) = 4x^3, find f′(7).

    4 · 3 · 7 · Power-rule differentiation

  4. 4. For f(x) = 6x^6, find f′(6).

    6 · 6 · 6 · Power-rule differentiation

  5. 5. For f(x) = 1x^2, find f′(5).

    1 · 2 · 5 · Power-rule differentiation

  6. 6. For f(x) = 1x^2, find f′(6).

    1 · 2 · 6 · Power-rule differentiation

  7. 7. For f(x) = 8x^3, find f′(3).

    8 · 3 · 3 · Power-rule differentiation

  8. 8. For f(x) = 12x^6, find f′(5).

    12 · 6 · 5 · Power-rule differentiation

  9. 9. For f(x) = 8x^2, find f′(6).

    8 · 2 · 6 · Power-rule differentiation

  10. 10. For f(x) = 3x^6, find f′(6).

    3 · 6 · 6 · Power-rule differentiation

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

    6 · 4 · 6 · Power-rule differentiation

  12. 12. For f(x) = 5x^3, find f′(1).

    5 · 3 · 1 · Power-rule differentiation
12 questions · Seed 54 · 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) = 12x^5, find f′(5).

    37500

    The power rule gives f′(x) = 60x^4. At x = 5, f′(5) = 37500.

  2. 2. For f(x) = 5x^6, find f′(4).

    30720

    The power rule gives f′(x) = 30x^5. At x = 4, f′(4) = 30720.

  3. 3. For f(x) = 4x^3, find f′(7).

    588

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

  4. 4. For f(x) = 6x^6, find f′(6).

    279936

    The power rule gives f′(x) = 36x^5. At x = 6, f′(6) = 279936.

  5. 5. For f(x) = 1x^2, find f′(5).

    10

    The power rule gives f′(x) = 2x^1. At x = 5, f′(5) = 10.

  6. 6. For f(x) = 1x^2, find f′(6).

    12

    The power rule gives f′(x) = 2x^1. At x = 6, f′(6) = 12.

  7. 7. For f(x) = 8x^3, find f′(3).

    216

    The power rule gives f′(x) = 24x^2. At x = 3, f′(3) = 216.

  8. 8. For f(x) = 12x^6, find f′(5).

    225000

    The power rule gives f′(x) = 72x^5. At x = 5, f′(5) = 225000.

  9. 9. For f(x) = 8x^2, find f′(6).

    96

    The power rule gives f′(x) = 16x^1. At x = 6, f′(6) = 96.

  10. 10. For f(x) = 3x^6, find f′(6).

    139968

    The power rule gives f′(x) = 18x^5. At x = 6, f′(6) = 139968.

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

    5184

    The power rule gives f′(x) = 24x^3. At x = 6, f′(6) = 5184.

  12. 12. For f(x) = 5x^3, find f′(1).

    15

    The power rule gives f′(x) = 15x^2. At x = 1, f′(1) = 15.

12 questions · Seed 54 · Age guidance, not curriculum certification