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

12 questions · Seed 104734 · 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^5, find f′(2).
80
The power rule gives f′(x) = 5x^4. At x = 2, f′(2) = 80.
2. For f(x) = 2x^4, find f′(3).
216
The power rule gives f′(x) = 8x^3. At x = 3, f′(3) = 216.
3. For f(x) = 8x^6, find f′(9).
2834352
The power rule gives f′(x) = 48x^5. At x = 9, f′(9) = 2834352.
4. For f(x) = 12x^2, find f′(4).
96
The power rule gives f′(x) = 24x^1. At x = 4, f′(4) = 96.
5. For f(x) = 3x^2, find f′(6).
36
The power rule gives f′(x) = 6x^1. At x = 6, f′(6) = 36.
6. For f(x) = 11x^5, find f′(7).
132055
The power rule gives f′(x) = 55x^4. At x = 7, f′(7) = 132055.
7. For f(x) = 4x^3, find f′(3).
108
The power rule gives f′(x) = 12x^2. At x = 3, f′(3) = 108.
8. For f(x) = 8x^5, find f′(5).
25000
The power rule gives f′(x) = 40x^4. At x = 5, f′(5) = 25000.
9. For f(x) = 8x^2, find f′(5).
80
The power rule gives f′(x) = 16x^1. At x = 5, f′(5) = 80.
10. For f(x) = 11x^2, find f′(7).
154
The power rule gives f′(x) = 22x^1. At x = 7, f′(7) = 154.
11. For f(x) = 12x^6, find f′(7).
1210104
The power rule gives f′(x) = 72x^5. At x = 7, f′(7) = 1210104.
12. For f(x) = 12x^4, find f′(1).
48
The power rule gives f′(x) = 48x^3. At x = 1, f′(1) = 48.

12 questions · Seed 104734 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 104734 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 1x^5, find f′(2).
80
The power rule gives f′(x) = 5x^4. At x = 2, f′(2) = 80.
2. For f(x) = 2x^4, find f′(3).
216
The power rule gives f′(x) = 8x^3. At x = 3, f′(3) = 216.
3. For f(x) = 8x^6, find f′(9).
2834352
The power rule gives f′(x) = 48x^5. At x = 9, f′(9) = 2834352.
4. For f(x) = 12x^2, find f′(4).
96
The power rule gives f′(x) = 24x^1. At x = 4, f′(4) = 96.
5. For f(x) = 3x^2, find f′(6).
36
The power rule gives f′(x) = 6x^1. At x = 6, f′(6) = 36.
6. For f(x) = 11x^5, find f′(7).
132055
The power rule gives f′(x) = 55x^4. At x = 7, f′(7) = 132055.
7. For f(x) = 4x^3, find f′(3).
108
The power rule gives f′(x) = 12x^2. At x = 3, f′(3) = 108.
8. For f(x) = 8x^5, find f′(5).
25000
The power rule gives f′(x) = 40x^4. At x = 5, f′(5) = 25000.
9. For f(x) = 8x^2, find f′(5).
80
The power rule gives f′(x) = 16x^1. At x = 5, f′(5) = 80.
10. For f(x) = 11x^2, find f′(7).
154
The power rule gives f′(x) = 22x^1. At x = 7, f′(7) = 154.
11. For f(x) = 12x^6, find f′(7).
1210104
The power rule gives f′(x) = 72x^5. At x = 7, f′(7) = 1210104.
12. For f(x) = 12x^4, find f′(1).
48
The power rule gives f′(x) = 48x^3. At x = 1, f′(1) = 48.

12 questions · Seed 104734 · Age guidance, not curriculum certification