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

12 questions · Seed 45 · 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^4, find f′(2).
192
The power rule gives f′(x) = 24x^3. At x = 2, f′(2) = 192.
2. For f(x) = 8x^2, find f′(5).
80
The power rule gives f′(x) = 16x^1. At x = 5, f′(5) = 80.
3. For f(x) = 8x^4, find f′(5).
4000
The power rule gives f′(x) = 32x^3. At x = 5, f′(5) = 4000.
4. For f(x) = 11x^3, find f′(7).
1617
The power rule gives f′(x) = 33x^2. At x = 7, f′(7) = 1617.
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) = 7x^5, find f′(9).
229635
The power rule gives f′(x) = 35x^4. At x = 9, f′(9) = 229635.
7. For f(x) = 8x^5, find f′(8).
163840
The power rule gives f′(x) = 40x^4. At x = 8, f′(8) = 163840.
8. For f(x) = 11x^4, find f′(6).
9504
The power rule gives f′(x) = 44x^3. At x = 6, f′(6) = 9504.
9. For f(x) = 8x^3, find f′(6).
864
The power rule gives f′(x) = 24x^2. At x = 6, f′(6) = 864.
10. For f(x) = 4x^3, find f′(8).
768
The power rule gives f′(x) = 12x^2. At x = 8, f′(8) = 768.
11. For f(x) = 11x^4, find f′(2).
352
The power rule gives f′(x) = 44x^3. At x = 2, f′(2) = 352.
12. For f(x) = 11x^5, find f′(4).
14080
The power rule gives f′(x) = 55x^4. At x = 4, f′(4) = 14080.

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 6x^4, find f′(2).
192
The power rule gives f′(x) = 24x^3. At x = 2, f′(2) = 192.
2. For f(x) = 8x^2, find f′(5).
80
The power rule gives f′(x) = 16x^1. At x = 5, f′(5) = 80.
3. For f(x) = 8x^4, find f′(5).
4000
The power rule gives f′(x) = 32x^3. At x = 5, f′(5) = 4000.
4. For f(x) = 11x^3, find f′(7).
1617
The power rule gives f′(x) = 33x^2. At x = 7, f′(7) = 1617.
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) = 7x^5, find f′(9).
229635
The power rule gives f′(x) = 35x^4. At x = 9, f′(9) = 229635.
7. For f(x) = 8x^5, find f′(8).
163840
The power rule gives f′(x) = 40x^4. At x = 8, f′(8) = 163840.
8. For f(x) = 11x^4, find f′(6).
9504
The power rule gives f′(x) = 44x^3. At x = 6, f′(6) = 9504.
9. For f(x) = 8x^3, find f′(6).
864
The power rule gives f′(x) = 24x^2. At x = 6, f′(6) = 864.
10. For f(x) = 4x^3, find f′(8).
768
The power rule gives f′(x) = 12x^2. At x = 8, f′(8) = 768.
11. For f(x) = 11x^4, find f′(2).
352
The power rule gives f′(x) = 44x^3. At x = 2, f′(2) = 352.
12. For f(x) = 11x^5, find f′(4).
14080
The power rule gives f′(x) = 55x^4. At x = 4, f′(4) = 14080.

12 questions · Seed 45 · Age guidance, not curriculum certification