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

12 questions · Seed 47 · 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) = 6x^2, find f′(4).
48
The power rule gives f′(x) = 12x^1. At x = 4, f′(4) = 48.
2. For f(x) = 11x^3, find f′(7).
1617
The power rule gives f′(x) = 33x^2. At x = 7, f′(7) = 1617.
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) = 10x^5, find f′(2).
800
The power rule gives f′(x) = 50x^4. At x = 2, f′(2) = 800.
5. For f(x) = 5x^4, find f′(5).
2500
The power rule gives f′(x) = 20x^3. At x = 5, f′(5) = 2500.
6. For f(x) = 3x^3, find f′(9).
729
The power rule gives f′(x) = 9x^2. At x = 9, f′(9) = 729.
7. For f(x) = 1x^4, find f′(3).
108
The power rule gives f′(x) = 4x^3. At x = 3, f′(3) = 108.
8. For f(x) = 10x^4, find f′(7).
13720
The power rule gives f′(x) = 40x^3. At x = 7, f′(7) = 13720.
9. For f(x) = 1x^6, find f′(9).
354294
The power rule gives f′(x) = 6x^5. At x = 9, f′(9) = 354294.
10. For f(x) = 4x^6, find f′(5).
75000
The power rule gives f′(x) = 24x^5. At x = 5, f′(5) = 75000.
11. For f(x) = 10x^2, find f′(3).
60
The power rule gives f′(x) = 20x^1. At x = 3, f′(3) = 60.
12. For f(x) = 5x^3, find f′(7).
735
The power rule gives f′(x) = 15x^2. At x = 7, f′(7) = 735.

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 6x^2, find f′(4).
48
The power rule gives f′(x) = 12x^1. At x = 4, f′(4) = 48.
2. For f(x) = 11x^3, find f′(7).
1617
The power rule gives f′(x) = 33x^2. At x = 7, f′(7) = 1617.
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) = 10x^5, find f′(2).
800
The power rule gives f′(x) = 50x^4. At x = 2, f′(2) = 800.
5. For f(x) = 5x^4, find f′(5).
2500
The power rule gives f′(x) = 20x^3. At x = 5, f′(5) = 2500.
6. For f(x) = 3x^3, find f′(9).
729
The power rule gives f′(x) = 9x^2. At x = 9, f′(9) = 729.
7. For f(x) = 1x^4, find f′(3).
108
The power rule gives f′(x) = 4x^3. At x = 3, f′(3) = 108.
8. For f(x) = 10x^4, find f′(7).
13720
The power rule gives f′(x) = 40x^3. At x = 7, f′(7) = 13720.
9. For f(x) = 1x^6, find f′(9).
354294
The power rule gives f′(x) = 6x^5. At x = 9, f′(9) = 354294.
10. For f(x) = 4x^6, find f′(5).
75000
The power rule gives f′(x) = 24x^5. At x = 5, f′(5) = 75000.
11. For f(x) = 10x^2, find f′(3).
60
The power rule gives f′(x) = 20x^1. At x = 3, f′(3) = 60.
12. For f(x) = 5x^3, find f′(7).
735
The power rule gives f′(x) = 15x^2. At x = 7, f′(7) = 735.

12 questions · Seed 47 · Age guidance, not curriculum certification