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

12 questions · Seed 104730 · 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^6, find f′(1).
60
The power rule gives f′(x) = 60x^5. At x = 1, f′(1) = 60.
2. For f(x) = 12x^5, find f′(1).
60
The power rule gives f′(x) = 60x^4. At x = 1, f′(1) = 60.
3. For f(x) = 6x^3, find f′(4).
288
The power rule gives f′(x) = 18x^2. At x = 4, f′(4) = 288.
4. For f(x) = 9x^3, find f′(8).
1728
The power rule gives f′(x) = 27x^2. At x = 8, f′(8) = 1728.
5. For f(x) = 10x^3, find f′(7).
1470
The power rule gives f′(x) = 30x^2. At x = 7, f′(7) = 1470.
6. For f(x) = 11x^2, find f′(6).
132
The power rule gives f′(x) = 22x^1. At x = 6, f′(6) = 132.
7. For f(x) = 12x^5, find f′(7).
144060
The power rule gives f′(x) = 60x^4. At x = 7, f′(7) = 144060.
8. For f(x) = 10x^2, find f′(5).
100
The power rule gives f′(x) = 20x^1. At x = 5, f′(5) = 100.
9. For f(x) = 12x^6, find f′(6).
559872
The power rule gives f′(x) = 72x^5. At x = 6, f′(6) = 559872.
10. For f(x) = 2x^6, find f′(6).
93312
The power rule gives f′(x) = 12x^5. At x = 6, f′(6) = 93312.
11. For f(x) = 5x^2, find f′(9).
90
The power rule gives f′(x) = 10x^1. At x = 9, f′(9) = 90.
12. For f(x) = 12x^3, find f′(1).
36
The power rule gives f′(x) = 36x^2. At x = 1, f′(1) = 36.

12 questions · Seed 104730 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 104730 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 10x^6, find f′(1).
60
The power rule gives f′(x) = 60x^5. At x = 1, f′(1) = 60.
2. For f(x) = 12x^5, find f′(1).
60
The power rule gives f′(x) = 60x^4. At x = 1, f′(1) = 60.
3. For f(x) = 6x^3, find f′(4).
288
The power rule gives f′(x) = 18x^2. At x = 4, f′(4) = 288.
4. For f(x) = 9x^3, find f′(8).
1728
The power rule gives f′(x) = 27x^2. At x = 8, f′(8) = 1728.
5. For f(x) = 10x^3, find f′(7).
1470
The power rule gives f′(x) = 30x^2. At x = 7, f′(7) = 1470.
6. For f(x) = 11x^2, find f′(6).
132
The power rule gives f′(x) = 22x^1. At x = 6, f′(6) = 132.
7. For f(x) = 12x^5, find f′(7).
144060
The power rule gives f′(x) = 60x^4. At x = 7, f′(7) = 144060.
8. For f(x) = 10x^2, find f′(5).
100
The power rule gives f′(x) = 20x^1. At x = 5, f′(5) = 100.
9. For f(x) = 12x^6, find f′(6).
559872
The power rule gives f′(x) = 72x^5. At x = 6, f′(6) = 559872.
10. For f(x) = 2x^6, find f′(6).
93312
The power rule gives f′(x) = 12x^5. At x = 6, f′(6) = 93312.
11. For f(x) = 5x^2, find f′(9).
90
The power rule gives f′(x) = 10x^1. At x = 9, f′(9) = 90.
12. For f(x) = 12x^3, find f′(1).
36
The power rule gives f′(x) = 36x^2. At x = 1, f′(1) = 36.

12 questions · Seed 104730 · Age guidance, not curriculum certification