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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^6, find f′(5).

    4 · 6 · 5 · Power-rule differentiation

  2. 2. For f(x) = 1x^4, find f′(3).

    1 · 4 · 3 · Power-rule differentiation

  3. 3. For f(x) = 2x^6, find f′(8).

    2 · 6 · 8 · Power-rule differentiation

  4. 4. For f(x) = 10x^2, find f′(7).

    10 · 2 · 7 · Power-rule differentiation

  5. 5. For f(x) = 1x^2, find f′(9).

    1 · 2 · 9 · Power-rule differentiation

  6. 6. For f(x) = 12x^6, find f′(5).

    12 · 6 · 5 · Power-rule differentiation

  7. 7. For f(x) = 11x^2, find f′(3).

    11 · 2 · 3 · Power-rule differentiation

  8. 8. For f(x) = 11x^2, find f′(4).

    11 · 2 · 4 · Power-rule differentiation

  9. 9. For f(x) = 1x^6, find f′(6).

    1 · 6 · 6 · Power-rule differentiation

  10. 10. For f(x) = 3x^5, find f′(8).

    3 · 5 · 8 · Power-rule differentiation

  11. 11. For f(x) = 8x^4, find f′(8).

    8 · 4 · 8 · Power-rule differentiation

  12. 12. For f(x) = 6x^2, find f′(9).

    6 · 2 · 9 · Power-rule differentiation
12 questions · Seed 50 · 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^6, find f′(5).

    75000

    The power rule gives f′(x) = 24x^5. At x = 5, f′(5) = 75000.

  2. 2. For f(x) = 1x^4, find f′(3).

    108

    The power rule gives f′(x) = 4x^3. At x = 3, f′(3) = 108.

  3. 3. For f(x) = 2x^6, find f′(8).

    393216

    The power rule gives f′(x) = 12x^5. At x = 8, f′(8) = 393216.

  4. 4. For f(x) = 10x^2, find f′(7).

    140

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

  5. 5. For f(x) = 1x^2, find f′(9).

    18

    The power rule gives f′(x) = 2x^1. At x = 9, f′(9) = 18.

  6. 6. For f(x) = 12x^6, find f′(5).

    225000

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

  7. 7. For f(x) = 11x^2, find f′(3).

    66

    The power rule gives f′(x) = 22x^1. At x = 3, f′(3) = 66.

  8. 8. For f(x) = 11x^2, find f′(4).

    88

    The power rule gives f′(x) = 22x^1. At x = 4, f′(4) = 88.

  9. 9. For f(x) = 1x^6, find f′(6).

    46656

    The power rule gives f′(x) = 6x^5. At x = 6, f′(6) = 46656.

  10. 10. For f(x) = 3x^5, find f′(8).

    61440

    The power rule gives f′(x) = 15x^4. At x = 8, f′(8) = 61440.

  11. 11. For f(x) = 8x^4, find f′(8).

    16384

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

  12. 12. For f(x) = 6x^2, find f′(9).

    108

    The power rule gives f′(x) = 12x^1. At x = 9, f′(9) = 108.

12 questions · Seed 50 · 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^6, find f′(5).

    4 · 6 · 5 · Power-rule differentiation

  2. 2. For f(x) = 1x^4, find f′(3).

    1 · 4 · 3 · Power-rule differentiation

  3. 3. For f(x) = 2x^6, find f′(8).

    2 · 6 · 8 · Power-rule differentiation

  4. 4. For f(x) = 10x^2, find f′(7).

    10 · 2 · 7 · Power-rule differentiation

  5. 5. For f(x) = 1x^2, find f′(9).

    1 · 2 · 9 · Power-rule differentiation

  6. 6. For f(x) = 12x^6, find f′(5).

    12 · 6 · 5 · Power-rule differentiation

  7. 7. For f(x) = 11x^2, find f′(3).

    11 · 2 · 3 · Power-rule differentiation

  8. 8. For f(x) = 11x^2, find f′(4).

    11 · 2 · 4 · Power-rule differentiation

  9. 9. For f(x) = 1x^6, find f′(6).

    1 · 6 · 6 · Power-rule differentiation

  10. 10. For f(x) = 3x^5, find f′(8).

    3 · 5 · 8 · Power-rule differentiation

  11. 11. For f(x) = 8x^4, find f′(8).

    8 · 4 · 8 · Power-rule differentiation

  12. 12. For f(x) = 6x^2, find f′(9).

    6 · 2 · 9 · Power-rule differentiation
12 questions · Seed 50 · 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^6, find f′(5).

    75000

    The power rule gives f′(x) = 24x^5. At x = 5, f′(5) = 75000.

  2. 2. For f(x) = 1x^4, find f′(3).

    108

    The power rule gives f′(x) = 4x^3. At x = 3, f′(3) = 108.

  3. 3. For f(x) = 2x^6, find f′(8).

    393216

    The power rule gives f′(x) = 12x^5. At x = 8, f′(8) = 393216.

  4. 4. For f(x) = 10x^2, find f′(7).

    140

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

  5. 5. For f(x) = 1x^2, find f′(9).

    18

    The power rule gives f′(x) = 2x^1. At x = 9, f′(9) = 18.

  6. 6. For f(x) = 12x^6, find f′(5).

    225000

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

  7. 7. For f(x) = 11x^2, find f′(3).

    66

    The power rule gives f′(x) = 22x^1. At x = 3, f′(3) = 66.

  8. 8. For f(x) = 11x^2, find f′(4).

    88

    The power rule gives f′(x) = 22x^1. At x = 4, f′(4) = 88.

  9. 9. For f(x) = 1x^6, find f′(6).

    46656

    The power rule gives f′(x) = 6x^5. At x = 6, f′(6) = 46656.

  10. 10. For f(x) = 3x^5, find f′(8).

    61440

    The power rule gives f′(x) = 15x^4. At x = 8, f′(8) = 61440.

  11. 11. For f(x) = 8x^4, find f′(8).

    16384

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

  12. 12. For f(x) = 6x^2, find f′(9).

    108

    The power rule gives f′(x) = 12x^1. At x = 9, f′(9) = 108.

12 questions · Seed 50 · Age guidance, not curriculum certification