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.

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 55 · 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^2, find f′(7).
14
The power rule gives f′(x) = 2x^1. At x = 7, f′(7) = 14.
2. For f(x) = 11x^4, find f′(4).
2816
The power rule gives f′(x) = 44x^3. At x = 4, f′(4) = 2816.
3. For f(x) = 7x^2, find f′(3).
42
The power rule gives f′(x) = 14x^1. At x = 3, f′(3) = 42.
4. For f(x) = 10x^4, find f′(7).
13720
The power rule gives f′(x) = 40x^3. At x = 7, f′(7) = 13720.
5. For f(x) = 7x^2, find f′(4).
56
The power rule gives f′(x) = 14x^1. At x = 4, f′(4) = 56.
6. For f(x) = 8x^6, find f′(6).
373248
The power rule gives f′(x) = 48x^5. At x = 6, f′(6) = 373248.
7. For f(x) = 10x^3, find f′(6).
1080
The power rule gives f′(x) = 30x^2. At x = 6, f′(6) = 1080.
8. For f(x) = 6x^3, find f′(3).
162
The power rule gives f′(x) = 18x^2. At x = 3, f′(3) = 162.
9. For f(x) = 2x^4, find f′(7).
2744
The power rule gives f′(x) = 8x^3. At x = 7, f′(7) = 2744.
10. For f(x) = 10x^3, find f′(5).
750
The power rule gives f′(x) = 30x^2. At x = 5, f′(5) = 750.
11. For f(x) = 4x^3, find f′(4).
192
The power rule gives f′(x) = 12x^2. At x = 4, f′(4) = 192.
12. For f(x) = 10x^6, find f′(4).
61440
The power rule gives f′(x) = 60x^5. At x = 4, f′(4) = 61440.

12 questions · Seed 55 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 55 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 1x^2, find f′(7).
14
The power rule gives f′(x) = 2x^1. At x = 7, f′(7) = 14.
2. For f(x) = 11x^4, find f′(4).
2816
The power rule gives f′(x) = 44x^3. At x = 4, f′(4) = 2816.
3. For f(x) = 7x^2, find f′(3).
42
The power rule gives f′(x) = 14x^1. At x = 3, f′(3) = 42.
4. For f(x) = 10x^4, find f′(7).
13720
The power rule gives f′(x) = 40x^3. At x = 7, f′(7) = 13720.
5. For f(x) = 7x^2, find f′(4).
56
The power rule gives f′(x) = 14x^1. At x = 4, f′(4) = 56.
6. For f(x) = 8x^6, find f′(6).
373248
The power rule gives f′(x) = 48x^5. At x = 6, f′(6) = 373248.
7. For f(x) = 10x^3, find f′(6).
1080
The power rule gives f′(x) = 30x^2. At x = 6, f′(6) = 1080.
8. For f(x) = 6x^3, find f′(3).
162
The power rule gives f′(x) = 18x^2. At x = 3, f′(3) = 162.
9. For f(x) = 2x^4, find f′(7).
2744
The power rule gives f′(x) = 8x^3. At x = 7, f′(7) = 2744.
10. For f(x) = 10x^3, find f′(5).
750
The power rule gives f′(x) = 30x^2. At x = 5, f′(5) = 750.
11. For f(x) = 4x^3, find f′(4).
192
The power rule gives f′(x) = 12x^2. At x = 4, f′(4) = 192.
12. For f(x) = 10x^6, find f′(4).
61440
The power rule gives f′(x) = 60x^5. At x = 4, f′(4) = 61440.

12 questions · Seed 55 · Age guidance, not curriculum certification