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

12 questions · Seed 43 · 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) = 9x^3, find f′(7).
1323
The power rule gives f′(x) = 27x^2. At x = 7, f′(7) = 1323.
2. For f(x) = 9x^3, find f′(5).
675
The power rule gives f′(x) = 27x^2. At x = 5, f′(5) = 675.
3. For f(x) = 5x^2, find f′(6).
60
The power rule gives f′(x) = 10x^1. At x = 6, f′(6) = 60.
4. For f(x) = 6x^5, find f′(4).
7680
The power rule gives f′(x) = 30x^4. At x = 4, f′(4) = 7680.
5. For f(x) = 2x^5, find f′(8).
40960
The power rule gives f′(x) = 10x^4. At x = 8, f′(8) = 40960.
6. For f(x) = 3x^6, find f′(4).
18432
The power rule gives f′(x) = 18x^5. At x = 4, f′(4) = 18432.
7. For f(x) = 8x^5, find f′(3).
3240
The power rule gives f′(x) = 40x^4. At x = 3, f′(3) = 3240.
8. For f(x) = 2x^4, find f′(7).
2744
The power rule gives f′(x) = 8x^3. At x = 7, f′(7) = 2744.
9. For f(x) = 1x^3, find f′(4).
48
The power rule gives f′(x) = 3x^2. At x = 4, f′(4) = 48.
10. For f(x) = 12x^6, find f′(5).
225000
The power rule gives f′(x) = 72x^5. At x = 5, f′(5) = 225000.
11. For f(x) = 6x^2, find f′(4).
48
The power rule gives f′(x) = 12x^1. At x = 4, f′(4) = 48.
12. For f(x) = 8x^4, find f′(4).
2048
The power rule gives f′(x) = 32x^3. At x = 4, f′(4) = 2048.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 9x^3, find f′(7).
1323
The power rule gives f′(x) = 27x^2. At x = 7, f′(7) = 1323.
2. For f(x) = 9x^3, find f′(5).
675
The power rule gives f′(x) = 27x^2. At x = 5, f′(5) = 675.
3. For f(x) = 5x^2, find f′(6).
60
The power rule gives f′(x) = 10x^1. At x = 6, f′(6) = 60.
4. For f(x) = 6x^5, find f′(4).
7680
The power rule gives f′(x) = 30x^4. At x = 4, f′(4) = 7680.
5. For f(x) = 2x^5, find f′(8).
40960
The power rule gives f′(x) = 10x^4. At x = 8, f′(8) = 40960.
6. For f(x) = 3x^6, find f′(4).
18432
The power rule gives f′(x) = 18x^5. At x = 4, f′(4) = 18432.
7. For f(x) = 8x^5, find f′(3).
3240
The power rule gives f′(x) = 40x^4. At x = 3, f′(3) = 3240.
8. For f(x) = 2x^4, find f′(7).
2744
The power rule gives f′(x) = 8x^3. At x = 7, f′(7) = 2744.
9. For f(x) = 1x^3, find f′(4).
48
The power rule gives f′(x) = 3x^2. At x = 4, f′(4) = 48.
10. For f(x) = 12x^6, find f′(5).
225000
The power rule gives f′(x) = 72x^5. At x = 5, f′(5) = 225000.
11. For f(x) = 6x^2, find f′(4).
48
The power rule gives f′(x) = 12x^1. At x = 4, f′(4) = 48.
12. For f(x) = 8x^4, find f′(4).
2048
The power rule gives f′(x) = 32x^3. At x = 4, f′(4) = 2048.

12 questions · Seed 43 · Age guidance, not curriculum certification