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

12 questions · Seed 57 · 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) = 2x^4, find f′(7).
2744
The power rule gives f′(x) = 8x^3. At x = 7, f′(7) = 2744.
2. For f(x) = 1x^4, find f′(8).
2048
The power rule gives f′(x) = 4x^3. At x = 8, f′(8) = 2048.
3. For f(x) = 4x^2, find f′(2).
16
The power rule gives f′(x) = 8x^1. At x = 2, f′(2) = 16.
4. For f(x) = 1x^2, find f′(9).
18
The power rule gives f′(x) = 2x^1. At x = 9, f′(9) = 18.
5. For f(x) = 6x^2, find f′(7).
84
The power rule gives f′(x) = 12x^1. At x = 7, f′(7) = 84.
6. For f(x) = 12x^2, find f′(4).
96
The power rule gives f′(x) = 24x^1. At x = 4, f′(4) = 96.
7. For f(x) = 11x^6, find f′(1).
66
The power rule gives f′(x) = 66x^5. At x = 1, f′(1) = 66.
8. For f(x) = 4x^5, find f′(5).
12500
The power rule gives f′(x) = 20x^4. At x = 5, f′(5) = 12500.
9. For f(x) = 11x^3, find f′(2).
132
The power rule gives f′(x) = 33x^2. At x = 2, f′(2) = 132.
10. For f(x) = 3x^2, find f′(7).
42
The power rule gives f′(x) = 6x^1. At x = 7, f′(7) = 42.
11. For f(x) = 12x^4, find f′(8).
24576
The power rule gives f′(x) = 48x^3. At x = 8, f′(8) = 24576.
12. For f(x) = 5x^4, find f′(2).
160
The power rule gives f′(x) = 20x^3. At x = 2, f′(2) = 160.

12 questions · Seed 57 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 57 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 2x^4, find f′(7).
2744
The power rule gives f′(x) = 8x^3. At x = 7, f′(7) = 2744.
2. For f(x) = 1x^4, find f′(8).
2048
The power rule gives f′(x) = 4x^3. At x = 8, f′(8) = 2048.
3. For f(x) = 4x^2, find f′(2).
16
The power rule gives f′(x) = 8x^1. At x = 2, f′(2) = 16.
4. For f(x) = 1x^2, find f′(9).
18
The power rule gives f′(x) = 2x^1. At x = 9, f′(9) = 18.
5. For f(x) = 6x^2, find f′(7).
84
The power rule gives f′(x) = 12x^1. At x = 7, f′(7) = 84.
6. For f(x) = 12x^2, find f′(4).
96
The power rule gives f′(x) = 24x^1. At x = 4, f′(4) = 96.
7. For f(x) = 11x^6, find f′(1).
66
The power rule gives f′(x) = 66x^5. At x = 1, f′(1) = 66.
8. For f(x) = 4x^5, find f′(5).
12500
The power rule gives f′(x) = 20x^4. At x = 5, f′(5) = 12500.
9. For f(x) = 11x^3, find f′(2).
132
The power rule gives f′(x) = 33x^2. At x = 2, f′(2) = 132.
10. For f(x) = 3x^2, find f′(7).
42
The power rule gives f′(x) = 6x^1. At x = 7, f′(7) = 42.
11. For f(x) = 12x^4, find f′(8).
24576
The power rule gives f′(x) = 48x^3. At x = 8, f′(8) = 24576.
12. For f(x) = 5x^4, find f′(2).
160
The power rule gives f′(x) = 20x^3. At x = 2, f′(2) = 160.

12 questions · Seed 57 · Age guidance, not curriculum certification