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

12 questions · Seed 52 · 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) = 8x^2, find f′(5).
80
The power rule gives f′(x) = 16x^1. At x = 5, f′(5) = 80.
2. For f(x) = 4x^6, find f′(7).
403368
The power rule gives f′(x) = 24x^5. At x = 7, f′(7) = 403368.
3. For f(x) = 10x^5, find f′(1).
50
The power rule gives f′(x) = 50x^4. At x = 1, f′(1) = 50.
4. For f(x) = 7x^5, find f′(3).
2835
The power rule gives f′(x) = 35x^4. At x = 3, f′(3) = 2835.
5. For f(x) = 6x^4, find f′(1).
24
The power rule gives f′(x) = 24x^3. At x = 1, f′(1) = 24.
6. For f(x) = 4x^6, find f′(3).
5832
The power rule gives f′(x) = 24x^5. At x = 3, f′(3) = 5832.
7. For f(x) = 6x^2, find f′(2).
24
The power rule gives f′(x) = 12x^1. At x = 2, f′(2) = 24.
8. For f(x) = 11x^5, find f′(6).
71280
The power rule gives f′(x) = 55x^4. At x = 6, f′(6) = 71280.
9. For f(x) = 9x^5, find f′(1).
45
The power rule gives f′(x) = 45x^4. At x = 1, f′(1) = 45.
10. For f(x) = 10x^3, find f′(7).
1470
The power rule gives f′(x) = 30x^2. At x = 7, f′(7) = 1470.
11. For f(x) = 12x^6, find f′(8).
2359296
The power rule gives f′(x) = 72x^5. At x = 8, f′(8) = 2359296.
12. For f(x) = 11x^6, find f′(6).
513216
The power rule gives f′(x) = 66x^5. At x = 6, f′(6) = 513216.

12 questions · Seed 52 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 52 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 8x^2, find f′(5).
80
The power rule gives f′(x) = 16x^1. At x = 5, f′(5) = 80.
2. For f(x) = 4x^6, find f′(7).
403368
The power rule gives f′(x) = 24x^5. At x = 7, f′(7) = 403368.
3. For f(x) = 10x^5, find f′(1).
50
The power rule gives f′(x) = 50x^4. At x = 1, f′(1) = 50.
4. For f(x) = 7x^5, find f′(3).
2835
The power rule gives f′(x) = 35x^4. At x = 3, f′(3) = 2835.
5. For f(x) = 6x^4, find f′(1).
24
The power rule gives f′(x) = 24x^3. At x = 1, f′(1) = 24.
6. For f(x) = 4x^6, find f′(3).
5832
The power rule gives f′(x) = 24x^5. At x = 3, f′(3) = 5832.
7. For f(x) = 6x^2, find f′(2).
24
The power rule gives f′(x) = 12x^1. At x = 2, f′(2) = 24.
8. For f(x) = 11x^5, find f′(6).
71280
The power rule gives f′(x) = 55x^4. At x = 6, f′(6) = 71280.
9. For f(x) = 9x^5, find f′(1).
45
The power rule gives f′(x) = 45x^4. At x = 1, f′(1) = 45.
10. For f(x) = 10x^3, find f′(7).
1470
The power rule gives f′(x) = 30x^2. At x = 7, f′(7) = 1470.
11. For f(x) = 12x^6, find f′(8).
2359296
The power rule gives f′(x) = 72x^5. At x = 8, f′(8) = 2359296.
12. For f(x) = 11x^6, find f′(6).
513216
The power rule gives f′(x) = 66x^5. At x = 6, f′(6) = 513216.

12 questions · Seed 52 · Age guidance, not curriculum certification