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

12 questions · Seed 104733 · 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) = 1x^3, find f′(3).
27
The power rule gives f′(x) = 3x^2. At x = 3, f′(3) = 27.
2. For f(x) = 2x^3, find f′(6).
216
The power rule gives f′(x) = 6x^2. At x = 6, f′(6) = 216.
3. For f(x) = 2x^5, find f′(9).
65610
The power rule gives f′(x) = 10x^4. At x = 9, f′(9) = 65610.
4. For f(x) = 2x^5, find f′(7).
24010
The power rule gives f′(x) = 10x^4. At x = 7, f′(7) = 24010.
5. For f(x) = 4x^2, find f′(9).
72
The power rule gives f′(x) = 8x^1. At x = 9, f′(9) = 72.
6. For f(x) = 11x^2, find f′(3).
66
The power rule gives f′(x) = 22x^1. At x = 3, f′(3) = 66.
7. For f(x) = 3x^5, find f′(3).
1215
The power rule gives f′(x) = 15x^4. At x = 3, f′(3) = 1215.
8. For f(x) = 1x^5, find f′(8).
20480
The power rule gives f′(x) = 5x^4. At x = 8, f′(8) = 20480.
9. For f(x) = 10x^2, find f′(3).
60
The power rule gives f′(x) = 20x^1. At x = 3, f′(3) = 60.
10. For f(x) = 10x^2, find f′(4).
80
The power rule gives f′(x) = 20x^1. At x = 4, f′(4) = 80.
11. For f(x) = 11x^6, find f′(1).
66
The power rule gives f′(x) = 66x^5. At x = 1, f′(1) = 66.
12. For f(x) = 6x^2, find f′(3).
36
The power rule gives f′(x) = 12x^1. At x = 3, f′(3) = 36.

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 1x^3, find f′(3).
27
The power rule gives f′(x) = 3x^2. At x = 3, f′(3) = 27.
2. For f(x) = 2x^3, find f′(6).
216
The power rule gives f′(x) = 6x^2. At x = 6, f′(6) = 216.
3. For f(x) = 2x^5, find f′(9).
65610
The power rule gives f′(x) = 10x^4. At x = 9, f′(9) = 65610.
4. For f(x) = 2x^5, find f′(7).
24010
The power rule gives f′(x) = 10x^4. At x = 7, f′(7) = 24010.
5. For f(x) = 4x^2, find f′(9).
72
The power rule gives f′(x) = 8x^1. At x = 9, f′(9) = 72.
6. For f(x) = 11x^2, find f′(3).
66
The power rule gives f′(x) = 22x^1. At x = 3, f′(3) = 66.
7. For f(x) = 3x^5, find f′(3).
1215
The power rule gives f′(x) = 15x^4. At x = 3, f′(3) = 1215.
8. For f(x) = 1x^5, find f′(8).
20480
The power rule gives f′(x) = 5x^4. At x = 8, f′(8) = 20480.
9. For f(x) = 10x^2, find f′(3).
60
The power rule gives f′(x) = 20x^1. At x = 3, f′(3) = 60.
10. For f(x) = 10x^2, find f′(4).
80
The power rule gives f′(x) = 20x^1. At x = 4, f′(4) = 80.
11. For f(x) = 11x^6, find f′(1).
66
The power rule gives f′(x) = 66x^5. At x = 1, f′(1) = 66.
12. For f(x) = 6x^2, find f′(3).
36
The power rule gives f′(x) = 12x^1. At x = 3, f′(3) = 36.

12 questions · Seed 104733 · Age guidance, not curriculum certification