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

12 questions · Seed 48 · 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) = 7x^5, find f′(1).
35
The power rule gives f′(x) = 35x^4. At x = 1, f′(1) = 35.
2. For f(x) = 1x^5, find f′(4).
1280
The power rule gives f′(x) = 5x^4. At x = 4, f′(4) = 1280.
3. For f(x) = 11x^5, find f′(9).
360855
The power rule gives f′(x) = 55x^4. At x = 9, f′(9) = 360855.
4. For f(x) = 6x^4, find f′(4).
1536
The power rule gives f′(x) = 24x^3. At x = 4, f′(4) = 1536.
5. For f(x) = 9x^5, find f′(4).
11520
The power rule gives f′(x) = 45x^4. At x = 4, f′(4) = 11520.
6. For f(x) = 9x^2, find f′(8).
144
The power rule gives f′(x) = 18x^1. At x = 8, f′(8) = 144.
7. For f(x) = 11x^2, find f′(8).
176
The power rule gives f′(x) = 22x^1. At x = 8, f′(8) = 176.
8. For f(x) = 2x^2, find f′(6).
24
The power rule gives f′(x) = 4x^1. At x = 6, f′(6) = 24.
9. For f(x) = 6x^2, find f′(4).
48
The power rule gives f′(x) = 12x^1. At x = 4, f′(4) = 48.
10. For f(x) = 11x^4, find f′(6).
9504
The power rule gives f′(x) = 44x^3. At x = 6, f′(6) = 9504.
11. For f(x) = 3x^2, find f′(1).
6
The power rule gives f′(x) = 6x^1. At x = 1, f′(1) = 6.
12. For f(x) = 4x^6, find f′(9).
1417176
The power rule gives f′(x) = 24x^5. At x = 9, f′(9) = 1417176.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 7x^5, find f′(1).
35
The power rule gives f′(x) = 35x^4. At x = 1, f′(1) = 35.
2. For f(x) = 1x^5, find f′(4).
1280
The power rule gives f′(x) = 5x^4. At x = 4, f′(4) = 1280.
3. For f(x) = 11x^5, find f′(9).
360855
The power rule gives f′(x) = 55x^4. At x = 9, f′(9) = 360855.
4. For f(x) = 6x^4, find f′(4).
1536
The power rule gives f′(x) = 24x^3. At x = 4, f′(4) = 1536.
5. For f(x) = 9x^5, find f′(4).
11520
The power rule gives f′(x) = 45x^4. At x = 4, f′(4) = 11520.
6. For f(x) = 9x^2, find f′(8).
144
The power rule gives f′(x) = 18x^1. At x = 8, f′(8) = 144.
7. For f(x) = 11x^2, find f′(8).
176
The power rule gives f′(x) = 22x^1. At x = 8, f′(8) = 176.
8. For f(x) = 2x^2, find f′(6).
24
The power rule gives f′(x) = 4x^1. At x = 6, f′(6) = 24.
9. For f(x) = 6x^2, find f′(4).
48
The power rule gives f′(x) = 12x^1. At x = 4, f′(4) = 48.
10. For f(x) = 11x^4, find f′(6).
9504
The power rule gives f′(x) = 44x^3. At x = 6, f′(6) = 9504.
11. For f(x) = 3x^2, find f′(1).
6
The power rule gives f′(x) = 6x^1. At x = 1, f′(1) = 6.
12. For f(x) = 4x^6, find f′(9).
1417176
The power rule gives f′(x) = 24x^5. At x = 9, f′(9) = 1417176.

12 questions · Seed 48 · Age guidance, not curriculum certification