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

12 questions · Seed 44 · 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) = 3x^5, find f′(2).
240
The power rule gives f′(x) = 15x^4. At x = 2, f′(2) = 240.
2. For f(x) = 9x^4, find f′(2).
288
The power rule gives f′(x) = 36x^3. At x = 2, f′(2) = 288.
3. For f(x) = 6x^4, find f′(4).
1536
The power rule gives f′(x) = 24x^3. At x = 4, f′(4) = 1536.
4. For f(x) = 5x^3, find f′(3).
135
The power rule gives f′(x) = 15x^2. At x = 3, f′(3) = 135.
5. For f(x) = 11x^5, find f′(4).
14080
The power rule gives f′(x) = 55x^4. At x = 4, f′(4) = 14080.
6. For f(x) = 3x^4, find f′(3).
324
The power rule gives f′(x) = 12x^3. At x = 3, f′(3) = 324.
7. For f(x) = 10x^4, find f′(8).
20480
The power rule gives f′(x) = 40x^3. At x = 8, f′(8) = 20480.
8. For f(x) = 7x^5, find f′(4).
8960
The power rule gives f′(x) = 35x^4. At x = 4, f′(4) = 8960.
9. For f(x) = 3x^6, find f′(3).
4374
The power rule gives f′(x) = 18x^5. At x = 3, f′(3) = 4374.
10. For f(x) = 9x^5, find f′(7).
108045
The power rule gives f′(x) = 45x^4. At x = 7, f′(7) = 108045.
11. For f(x) = 4x^3, find f′(2).
48
The power rule gives f′(x) = 12x^2. At x = 2, f′(2) = 48.
12. For f(x) = 11x^4, find f′(5).
5500
The power rule gives f′(x) = 44x^3. At x = 5, f′(5) = 5500.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 3x^5, find f′(2).
240
The power rule gives f′(x) = 15x^4. At x = 2, f′(2) = 240.
2. For f(x) = 9x^4, find f′(2).
288
The power rule gives f′(x) = 36x^3. At x = 2, f′(2) = 288.
3. For f(x) = 6x^4, find f′(4).
1536
The power rule gives f′(x) = 24x^3. At x = 4, f′(4) = 1536.
4. For f(x) = 5x^3, find f′(3).
135
The power rule gives f′(x) = 15x^2. At x = 3, f′(3) = 135.
5. For f(x) = 11x^5, find f′(4).
14080
The power rule gives f′(x) = 55x^4. At x = 4, f′(4) = 14080.
6. For f(x) = 3x^4, find f′(3).
324
The power rule gives f′(x) = 12x^3. At x = 3, f′(3) = 324.
7. For f(x) = 10x^4, find f′(8).
20480
The power rule gives f′(x) = 40x^3. At x = 8, f′(8) = 20480.
8. For f(x) = 7x^5, find f′(4).
8960
The power rule gives f′(x) = 35x^4. At x = 4, f′(4) = 8960.
9. For f(x) = 3x^6, find f′(3).
4374
The power rule gives f′(x) = 18x^5. At x = 3, f′(3) = 4374.
10. For f(x) = 9x^5, find f′(7).
108045
The power rule gives f′(x) = 45x^4. At x = 7, f′(7) = 108045.
11. For f(x) = 4x^3, find f′(2).
48
The power rule gives f′(x) = 12x^2. At x = 2, f′(2) = 48.
12. For f(x) = 11x^4, find f′(5).
5500
The power rule gives f′(x) = 44x^3. At x = 5, f′(5) = 5500.

12 questions · Seed 44 · Age guidance, not curriculum certification