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

Take your time. Show your thinking.

1. For f(x) = 9x^2, find f′(5).
9 · 2 · 5 · Power-rule differentiation
2. For f(x) = 9x^3, find f′(5).
9 · 3 · 5 · Power-rule differentiation
3. For f(x) = 9x^4, find f′(3).
9 · 4 · 3 · Power-rule differentiation
4. For f(x) = 1x^4, find f′(5).
1 · 4 · 5 · Power-rule differentiation
5. For f(x) = 6x^2, find f′(8).
6 · 2 · 8 · Power-rule differentiation
6. For f(x) = 5x^4, find f′(7).
5 · 4 · 7 · Power-rule differentiation
7. For f(x) = 3x^6, find f′(3).
3 · 6 · 3 · Power-rule differentiation
8. For f(x) = 6x^4, find f′(6).
6 · 4 · 6 · Power-rule differentiation
9. For f(x) = 7x^5, find f′(1).
7 · 5 · 1 · Power-rule differentiation
10. For f(x) = 7x^3, find f′(5).
7 · 3 · 5 · Power-rule differentiation
11. For f(x) = 12x^2, find f′(3).
12 · 2 · 3 · Power-rule differentiation
12. For f(x) = 1x^5, find f′(8).
1 · 5 · 8 · Power-rule differentiation

12 questions · Seed 104729 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 9x^2, find f′(5).
90
The power rule gives f′(x) = 18x^1. At x = 5, f′(5) = 90.
2. For f(x) = 9x^3, find f′(5).
675
The power rule gives f′(x) = 27x^2. At x = 5, f′(5) = 675.
3. For f(x) = 9x^4, find f′(3).
972
The power rule gives f′(x) = 36x^3. At x = 3, f′(3) = 972.
4. For f(x) = 1x^4, find f′(5).
500
The power rule gives f′(x) = 4x^3. At x = 5, f′(5) = 500.
5. For f(x) = 6x^2, find f′(8).
96
The power rule gives f′(x) = 12x^1. At x = 8, f′(8) = 96.
6. For f(x) = 5x^4, find f′(7).
6860
The power rule gives f′(x) = 20x^3. At x = 7, f′(7) = 6860.
7. For f(x) = 3x^6, find f′(3).
4374
The power rule gives f′(x) = 18x^5. At x = 3, f′(3) = 4374.
8. For f(x) = 6x^4, find f′(6).
5184
The power rule gives f′(x) = 24x^3. At x = 6, f′(6) = 5184.
9. For f(x) = 7x^5, find f′(1).
35
The power rule gives f′(x) = 35x^4. At x = 1, f′(1) = 35.
10. For f(x) = 7x^3, find f′(5).
525
The power rule gives f′(x) = 21x^2. At x = 5, f′(5) = 525.
11. For f(x) = 12x^2, find f′(3).
72
The power rule gives f′(x) = 24x^1. At x = 3, f′(3) = 72.
12. For f(x) = 1x^5, find f′(8).
20480
The power rule gives f′(x) = 5x^4. At x = 8, f′(8) = 20480.

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

1. For f(x) = 9x^2, find f′(5).
9 · 2 · 5 · Power-rule differentiation
2. For f(x) = 9x^3, find f′(5).
9 · 3 · 5 · Power-rule differentiation
3. For f(x) = 9x^4, find f′(3).
9 · 4 · 3 · Power-rule differentiation
4. For f(x) = 1x^4, find f′(5).
1 · 4 · 5 · Power-rule differentiation
5. For f(x) = 6x^2, find f′(8).
6 · 2 · 8 · Power-rule differentiation
6. For f(x) = 5x^4, find f′(7).
5 · 4 · 7 · Power-rule differentiation
7. For f(x) = 3x^6, find f′(3).
3 · 6 · 3 · Power-rule differentiation
8. For f(x) = 6x^4, find f′(6).
6 · 4 · 6 · Power-rule differentiation
9. For f(x) = 7x^5, find f′(1).
7 · 5 · 1 · Power-rule differentiation
10. For f(x) = 7x^3, find f′(5).
7 · 3 · 5 · Power-rule differentiation
11. For f(x) = 12x^2, find f′(3).
12 · 2 · 3 · Power-rule differentiation
12. For f(x) = 1x^5, find f′(8).
1 · 5 · 8 · Power-rule differentiation

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 9x^2, find f′(5).
90
The power rule gives f′(x) = 18x^1. At x = 5, f′(5) = 90.
2. For f(x) = 9x^3, find f′(5).
675
The power rule gives f′(x) = 27x^2. At x = 5, f′(5) = 675.
3. For f(x) = 9x^4, find f′(3).
972
The power rule gives f′(x) = 36x^3. At x = 3, f′(3) = 972.
4. For f(x) = 1x^4, find f′(5).
500
The power rule gives f′(x) = 4x^3. At x = 5, f′(5) = 500.
5. For f(x) = 6x^2, find f′(8).
96
The power rule gives f′(x) = 12x^1. At x = 8, f′(8) = 96.
6. For f(x) = 5x^4, find f′(7).
6860
The power rule gives f′(x) = 20x^3. At x = 7, f′(7) = 6860.
7. For f(x) = 3x^6, find f′(3).
4374
The power rule gives f′(x) = 18x^5. At x = 3, f′(3) = 4374.
8. For f(x) = 6x^4, find f′(6).
5184
The power rule gives f′(x) = 24x^3. At x = 6, f′(6) = 5184.
9. For f(x) = 7x^5, find f′(1).
35
The power rule gives f′(x) = 35x^4. At x = 1, f′(1) = 35.
10. For f(x) = 7x^3, find f′(5).
525
The power rule gives f′(x) = 21x^2. At x = 5, f′(5) = 525.
11. For f(x) = 12x^2, find f′(3).
72
The power rule gives f′(x) = 24x^1. At x = 3, f′(3) = 72.
12. For f(x) = 1x^5, find f′(8).
20480
The power rule gives f′(x) = 5x^4. At x = 8, f′(8) = 20480.

12 questions · Seed 104729 · Age guidance, not curriculum certification