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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^3, find f′(8).

    12 · 3 · 8 · Power-rule differentiation

  2. 2. For f(x) = 2x^4, find f′(7).

    2 · 4 · 7 · Power-rule differentiation

  3. 3. For f(x) = 9x^6, find f′(6).

    9 · 6 · 6 · Power-rule differentiation

  4. 4. For f(x) = 11x^2, find f′(3).

    11 · 2 · 3 · Power-rule differentiation

  5. 5. For f(x) = 8x^5, find f′(4).

    8 · 5 · 4 · Power-rule differentiation

  6. 6. For f(x) = 2x^3, find f′(5).

    2 · 3 · 5 · Power-rule differentiation

  7. 7. For f(x) = 6x^5, find f′(2).

    6 · 5 · 2 · Power-rule differentiation

  8. 8. For f(x) = 9x^6, find f′(8).

    9 · 6 · 8 · Power-rule differentiation

  9. 9. For f(x) = 2x^5, find f′(2).

    2 · 5 · 2 · Power-rule differentiation

  10. 10. For f(x) = 2x^3, find f′(1).

    2 · 3 · 1 · Power-rule differentiation

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

    8 · 3 · 3 · Power-rule differentiation

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

    3 · 3 · 3 · Power-rule differentiation
12 questions · Seed 56 · 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^3, find f′(8).

    2304

    The power rule gives f′(x) = 36x^2. At x = 8, f′(8) = 2304.

  2. 2. For f(x) = 2x^4, find f′(7).

    2744

    The power rule gives f′(x) = 8x^3. At x = 7, f′(7) = 2744.

  3. 3. For f(x) = 9x^6, find f′(6).

    419904

    The power rule gives f′(x) = 54x^5. At x = 6, f′(6) = 419904.

  4. 4. For f(x) = 11x^2, find f′(3).

    66

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

  5. 5. For f(x) = 8x^5, find f′(4).

    10240

    The power rule gives f′(x) = 40x^4. At x = 4, f′(4) = 10240.

  6. 6. For f(x) = 2x^3, find f′(5).

    150

    The power rule gives f′(x) = 6x^2. At x = 5, f′(5) = 150.

  7. 7. For f(x) = 6x^5, find f′(2).

    480

    The power rule gives f′(x) = 30x^4. At x = 2, f′(2) = 480.

  8. 8. For f(x) = 9x^6, find f′(8).

    1769472

    The power rule gives f′(x) = 54x^5. At x = 8, f′(8) = 1769472.

  9. 9. For f(x) = 2x^5, find f′(2).

    160

    The power rule gives f′(x) = 10x^4. At x = 2, f′(2) = 160.

  10. 10. For f(x) = 2x^3, find f′(1).

    6

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

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

    216

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

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

    81

    The power rule gives f′(x) = 9x^2. At x = 3, f′(3) = 81.

12 questions · Seed 56 · 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^3, find f′(8).

    12 · 3 · 8 · Power-rule differentiation

  2. 2. For f(x) = 2x^4, find f′(7).

    2 · 4 · 7 · Power-rule differentiation

  3. 3. For f(x) = 9x^6, find f′(6).

    9 · 6 · 6 · Power-rule differentiation

  4. 4. For f(x) = 11x^2, find f′(3).

    11 · 2 · 3 · Power-rule differentiation

  5. 5. For f(x) = 8x^5, find f′(4).

    8 · 5 · 4 · Power-rule differentiation

  6. 6. For f(x) = 2x^3, find f′(5).

    2 · 3 · 5 · Power-rule differentiation

  7. 7. For f(x) = 6x^5, find f′(2).

    6 · 5 · 2 · Power-rule differentiation

  8. 8. For f(x) = 9x^6, find f′(8).

    9 · 6 · 8 · Power-rule differentiation

  9. 9. For f(x) = 2x^5, find f′(2).

    2 · 5 · 2 · Power-rule differentiation

  10. 10. For f(x) = 2x^3, find f′(1).

    2 · 3 · 1 · Power-rule differentiation

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

    8 · 3 · 3 · Power-rule differentiation

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

    3 · 3 · 3 · Power-rule differentiation
12 questions · Seed 56 · 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^3, find f′(8).

    2304

    The power rule gives f′(x) = 36x^2. At x = 8, f′(8) = 2304.

  2. 2. For f(x) = 2x^4, find f′(7).

    2744

    The power rule gives f′(x) = 8x^3. At x = 7, f′(7) = 2744.

  3. 3. For f(x) = 9x^6, find f′(6).

    419904

    The power rule gives f′(x) = 54x^5. At x = 6, f′(6) = 419904.

  4. 4. For f(x) = 11x^2, find f′(3).

    66

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

  5. 5. For f(x) = 8x^5, find f′(4).

    10240

    The power rule gives f′(x) = 40x^4. At x = 4, f′(4) = 10240.

  6. 6. For f(x) = 2x^3, find f′(5).

    150

    The power rule gives f′(x) = 6x^2. At x = 5, f′(5) = 150.

  7. 7. For f(x) = 6x^5, find f′(2).

    480

    The power rule gives f′(x) = 30x^4. At x = 2, f′(2) = 480.

  8. 8. For f(x) = 9x^6, find f′(8).

    1769472

    The power rule gives f′(x) = 54x^5. At x = 8, f′(8) = 1769472.

  9. 9. For f(x) = 2x^5, find f′(2).

    160

    The power rule gives f′(x) = 10x^4. At x = 2, f′(2) = 160.

  10. 10. For f(x) = 2x^3, find f′(1).

    6

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

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

    216

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

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

    81

    The power rule gives f′(x) = 9x^2. At x = 3, f′(3) = 81.

12 questions · Seed 56 · Age guidance, not curriculum certification