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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) = 10x^3, find f′(7).

    10 · 3 · 7 · Power-rule differentiation

  2. 2. For f(x) = 1x^2, find f′(5).

    1 · 2 · 5 · Power-rule differentiation

  3. 3. For f(x) = 6x^6, find f′(7).

    6 · 6 · 7 · Power-rule differentiation

  4. 4. For f(x) = 7x^4, find f′(1).

    7 · 4 · 1 · Power-rule differentiation

  5. 5. For f(x) = 9x^4, find f′(4).

    9 · 4 · 4 · Power-rule differentiation

  6. 6. For f(x) = 2x^6, find f′(9).

    2 · 6 · 9 · Power-rule differentiation

  7. 7. For f(x) = 3x^5, find f′(8).

    3 · 5 · 8 · Power-rule differentiation

  8. 8. For f(x) = 10x^5, find f′(7).

    10 · 5 · 7 · Power-rule differentiation

  9. 9. For f(x) = 5x^6, find f′(4).

    5 · 6 · 4 · Power-rule differentiation

  10. 10. For f(x) = 2x^3, find f′(6).

    2 · 3 · 6 · Power-rule differentiation

  11. 11. For f(x) = 4x^3, find f′(8).

    4 · 3 · 8 · Power-rule differentiation

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

    9 · 4 · 3 · Power-rule differentiation
12 questions · Seed 104735 · 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) = 10x^3, find f′(7).

    1470

    The power rule gives f′(x) = 30x^2. At x = 7, f′(7) = 1470.

  2. 2. For f(x) = 1x^2, find f′(5).

    10

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

  3. 3. For f(x) = 6x^6, find f′(7).

    605052

    The power rule gives f′(x) = 36x^5. At x = 7, f′(7) = 605052.

  4. 4. For f(x) = 7x^4, find f′(1).

    28

    The power rule gives f′(x) = 28x^3. At x = 1, f′(1) = 28.

  5. 5. For f(x) = 9x^4, find f′(4).

    2304

    The power rule gives f′(x) = 36x^3. At x = 4, f′(4) = 2304.

  6. 6. For f(x) = 2x^6, find f′(9).

    708588

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

  7. 7. For f(x) = 3x^5, find f′(8).

    61440

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

  8. 8. For f(x) = 10x^5, find f′(7).

    120050

    The power rule gives f′(x) = 50x^4. At x = 7, f′(7) = 120050.

  9. 9. For f(x) = 5x^6, find f′(4).

    30720

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

  10. 10. For f(x) = 2x^3, find f′(6).

    216

    The power rule gives f′(x) = 6x^2. At x = 6, f′(6) = 216.

  11. 11. For f(x) = 4x^3, find f′(8).

    768

    The power rule gives f′(x) = 12x^2. At x = 8, f′(8) = 768.

  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 104735 · 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) = 10x^3, find f′(7).

    10 · 3 · 7 · Power-rule differentiation

  2. 2. For f(x) = 1x^2, find f′(5).

    1 · 2 · 5 · Power-rule differentiation

  3. 3. For f(x) = 6x^6, find f′(7).

    6 · 6 · 7 · Power-rule differentiation

  4. 4. For f(x) = 7x^4, find f′(1).

    7 · 4 · 1 · Power-rule differentiation

  5. 5. For f(x) = 9x^4, find f′(4).

    9 · 4 · 4 · Power-rule differentiation

  6. 6. For f(x) = 2x^6, find f′(9).

    2 · 6 · 9 · Power-rule differentiation

  7. 7. For f(x) = 3x^5, find f′(8).

    3 · 5 · 8 · Power-rule differentiation

  8. 8. For f(x) = 10x^5, find f′(7).

    10 · 5 · 7 · Power-rule differentiation

  9. 9. For f(x) = 5x^6, find f′(4).

    5 · 6 · 4 · Power-rule differentiation

  10. 10. For f(x) = 2x^3, find f′(6).

    2 · 3 · 6 · Power-rule differentiation

  11. 11. For f(x) = 4x^3, find f′(8).

    4 · 3 · 8 · Power-rule differentiation

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

    9 · 4 · 3 · Power-rule differentiation
12 questions · Seed 104735 · 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) = 10x^3, find f′(7).

    1470

    The power rule gives f′(x) = 30x^2. At x = 7, f′(7) = 1470.

  2. 2. For f(x) = 1x^2, find f′(5).

    10

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

  3. 3. For f(x) = 6x^6, find f′(7).

    605052

    The power rule gives f′(x) = 36x^5. At x = 7, f′(7) = 605052.

  4. 4. For f(x) = 7x^4, find f′(1).

    28

    The power rule gives f′(x) = 28x^3. At x = 1, f′(1) = 28.

  5. 5. For f(x) = 9x^4, find f′(4).

    2304

    The power rule gives f′(x) = 36x^3. At x = 4, f′(4) = 2304.

  6. 6. For f(x) = 2x^6, find f′(9).

    708588

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

  7. 7. For f(x) = 3x^5, find f′(8).

    61440

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

  8. 8. For f(x) = 10x^5, find f′(7).

    120050

    The power rule gives f′(x) = 50x^4. At x = 7, f′(7) = 120050.

  9. 9. For f(x) = 5x^6, find f′(4).

    30720

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

  10. 10. For f(x) = 2x^3, find f′(6).

    216

    The power rule gives f′(x) = 6x^2. At x = 6, f′(6) = 216.

  11. 11. For f(x) = 4x^3, find f′(8).

    768

    The power rule gives f′(x) = 12x^2. At x = 8, f′(8) = 768.

  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 104735 · Age guidance, not curriculum certification