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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) = 8x^4, find f′(6).

    8 · 4 · 6 · Power-rule differentiation

  2. 2. For f(x) = 6x^6, find f′(1).

    6 · 6 · 1 · Power-rule differentiation

  3. 3. For f(x) = 2x^6, find f′(9).

    2 · 6 · 9 · Power-rule differentiation

  4. 4. For f(x) = 8x^2, find f′(9).

    8 · 2 · 9 · Power-rule differentiation

  5. 5. For f(x) = 4x^2, find f′(4).

    4 · 2 · 4 · Power-rule differentiation

  6. 6. For f(x) = 1x^3, find f′(7).

    1 · 3 · 7 · Power-rule differentiation

  7. 7. For f(x) = 9x^6, find f′(4).

    9 · 6 · 4 · Power-rule differentiation

  8. 8. For f(x) = 11x^4, find f′(3).

    11 · 4 · 3 · Power-rule differentiation

  9. 9. For f(x) = 9x^2, find f′(7).

    9 · 2 · 7 · Power-rule differentiation

  10. 10. For f(x) = 2x^6, find f′(7).

    2 · 6 · 7 · Power-rule differentiation

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

    4 · 4 · 4 · Power-rule differentiation

  12. 12. For f(x) = 9x^4, find f′(3).

    9 · 4 · 3 · Power-rule differentiation
12 questions · Seed 104732 · 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) = 8x^4, find f′(6).

    6912

    The power rule gives f′(x) = 32x^3. At x = 6, f′(6) = 6912.

  2. 2. For f(x) = 6x^6, find f′(1).

    36

    The power rule gives f′(x) = 36x^5. At x = 1, f′(1) = 36.

  3. 3. For f(x) = 2x^6, find f′(9).

    708588

    The power rule gives f′(x) = 12x^5. At x = 9, f′(9) = 708588.

  4. 4. For f(x) = 8x^2, find f′(9).

    144

    The power rule gives f′(x) = 16x^1. At x = 9, f′(9) = 144.

  5. 5. For f(x) = 4x^2, find f′(4).

    32

    The power rule gives f′(x) = 8x^1. At x = 4, f′(4) = 32.

  6. 6. For f(x) = 1x^3, find f′(7).

    147

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

  7. 7. For f(x) = 9x^6, find f′(4).

    55296

    The power rule gives f′(x) = 54x^5. At x = 4, f′(4) = 55296.

  8. 8. For f(x) = 11x^4, find f′(3).

    1188

    The power rule gives f′(x) = 44x^3. At x = 3, f′(3) = 1188.

  9. 9. For f(x) = 9x^2, find f′(7).

    126

    The power rule gives f′(x) = 18x^1. At x = 7, f′(7) = 126.

  10. 10. For f(x) = 2x^6, find f′(7).

    201684

    The power rule gives f′(x) = 12x^5. At x = 7, f′(7) = 201684.

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

    1024

    The power rule gives f′(x) = 16x^3. At x = 4, f′(4) = 1024.

  12. 12. For f(x) = 9x^4, find f′(3).

    972

    The power rule gives f′(x) = 36x^3. At x = 3, f′(3) = 972.

12 questions · Seed 104732 · 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) = 8x^4, find f′(6).

    8 · 4 · 6 · Power-rule differentiation

  2. 2. For f(x) = 6x^6, find f′(1).

    6 · 6 · 1 · Power-rule differentiation

  3. 3. For f(x) = 2x^6, find f′(9).

    2 · 6 · 9 · Power-rule differentiation

  4. 4. For f(x) = 8x^2, find f′(9).

    8 · 2 · 9 · Power-rule differentiation

  5. 5. For f(x) = 4x^2, find f′(4).

    4 · 2 · 4 · Power-rule differentiation

  6. 6. For f(x) = 1x^3, find f′(7).

    1 · 3 · 7 · Power-rule differentiation

  7. 7. For f(x) = 9x^6, find f′(4).

    9 · 6 · 4 · Power-rule differentiation

  8. 8. For f(x) = 11x^4, find f′(3).

    11 · 4 · 3 · Power-rule differentiation

  9. 9. For f(x) = 9x^2, find f′(7).

    9 · 2 · 7 · Power-rule differentiation

  10. 10. For f(x) = 2x^6, find f′(7).

    2 · 6 · 7 · Power-rule differentiation

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

    4 · 4 · 4 · Power-rule differentiation

  12. 12. For f(x) = 9x^4, find f′(3).

    9 · 4 · 3 · Power-rule differentiation
12 questions · Seed 104732 · 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) = 8x^4, find f′(6).

    6912

    The power rule gives f′(x) = 32x^3. At x = 6, f′(6) = 6912.

  2. 2. For f(x) = 6x^6, find f′(1).

    36

    The power rule gives f′(x) = 36x^5. At x = 1, f′(1) = 36.

  3. 3. For f(x) = 2x^6, find f′(9).

    708588

    The power rule gives f′(x) = 12x^5. At x = 9, f′(9) = 708588.

  4. 4. For f(x) = 8x^2, find f′(9).

    144

    The power rule gives f′(x) = 16x^1. At x = 9, f′(9) = 144.

  5. 5. For f(x) = 4x^2, find f′(4).

    32

    The power rule gives f′(x) = 8x^1. At x = 4, f′(4) = 32.

  6. 6. For f(x) = 1x^3, find f′(7).

    147

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

  7. 7. For f(x) = 9x^6, find f′(4).

    55296

    The power rule gives f′(x) = 54x^5. At x = 4, f′(4) = 55296.

  8. 8. For f(x) = 11x^4, find f′(3).

    1188

    The power rule gives f′(x) = 44x^3. At x = 3, f′(3) = 1188.

  9. 9. For f(x) = 9x^2, find f′(7).

    126

    The power rule gives f′(x) = 18x^1. At x = 7, f′(7) = 126.

  10. 10. For f(x) = 2x^6, find f′(7).

    201684

    The power rule gives f′(x) = 12x^5. At x = 7, f′(7) = 201684.

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

    1024

    The power rule gives f′(x) = 16x^3. At x = 4, f′(4) = 1024.

  12. 12. For f(x) = 9x^4, find f′(3).

    972

    The power rule gives f′(x) = 36x^3. At x = 3, f′(3) = 972.

12 questions · Seed 104732 · Age guidance, not curriculum certification