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

12 questions · Seed 51 · 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) = 10x^5, find f′(2).
800
The power rule gives f′(x) = 50x^4. At x = 2, f′(2) = 800.
2. For f(x) = 9x^5, find f′(8).
184320
The power rule gives f′(x) = 45x^4. At x = 8, f′(8) = 184320.
3. For f(x) = 3x^5, find f′(7).
36015
The power rule gives f′(x) = 15x^4. At x = 7, f′(7) = 36015.
4. For f(x) = 4x^5, find f′(5).
12500
The power rule gives f′(x) = 20x^4. At x = 5, f′(5) = 12500.
5. For f(x) = 1x^2, find f′(5).
10
The power rule gives f′(x) = 2x^1. At x = 5, f′(5) = 10.
6. For f(x) = 11x^4, find f′(1).
44
The power rule gives f′(x) = 44x^3. At x = 1, f′(1) = 44.
7. For f(x) = 6x^6, find f′(2).
1152
The power rule gives f′(x) = 36x^5. At x = 2, f′(2) = 1152.
8. For f(x) = 1x^3, find f′(9).
243
The power rule gives f′(x) = 3x^2. At x = 9, f′(9) = 243.
9. For f(x) = 3x^6, find f′(1).
18
The power rule gives f′(x) = 18x^5. At x = 1, f′(1) = 18.
10. For f(x) = 11x^6, find f′(5).
206250
The power rule gives f′(x) = 66x^5. At x = 5, f′(5) = 206250.
11. For f(x) = 3x^5, find f′(5).
9375
The power rule gives f′(x) = 15x^4. At x = 5, f′(5) = 9375.
12. For f(x) = 3x^6, find f′(9).
1062882
The power rule gives f′(x) = 18x^5. At x = 9, f′(9) = 1062882.

12 questions · Seed 51 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 51 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 10x^5, find f′(2).
800
The power rule gives f′(x) = 50x^4. At x = 2, f′(2) = 800.
2. For f(x) = 9x^5, find f′(8).
184320
The power rule gives f′(x) = 45x^4. At x = 8, f′(8) = 184320.
3. For f(x) = 3x^5, find f′(7).
36015
The power rule gives f′(x) = 15x^4. At x = 7, f′(7) = 36015.
4. For f(x) = 4x^5, find f′(5).
12500
The power rule gives f′(x) = 20x^4. At x = 5, f′(5) = 12500.
5. For f(x) = 1x^2, find f′(5).
10
The power rule gives f′(x) = 2x^1. At x = 5, f′(5) = 10.
6. For f(x) = 11x^4, find f′(1).
44
The power rule gives f′(x) = 44x^3. At x = 1, f′(1) = 44.
7. For f(x) = 6x^6, find f′(2).
1152
The power rule gives f′(x) = 36x^5. At x = 2, f′(2) = 1152.
8. For f(x) = 1x^3, find f′(9).
243
The power rule gives f′(x) = 3x^2. At x = 9, f′(9) = 243.
9. For f(x) = 3x^6, find f′(1).
18
The power rule gives f′(x) = 18x^5. At x = 1, f′(1) = 18.
10. For f(x) = 11x^6, find f′(5).
206250
The power rule gives f′(x) = 66x^5. At x = 5, f′(5) = 206250.
11. For f(x) = 3x^5, find f′(5).
9375
The power rule gives f′(x) = 15x^4. At x = 5, f′(5) = 9375.
12. For f(x) = 3x^6, find f′(9).
1062882
The power rule gives f′(x) = 18x^5. At x = 9, f′(9) = 1062882.

12 questions · Seed 51 · Age guidance, not curriculum certification