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.

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 104731 · 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) = 6x^6, find f′(6).
279936
The power rule gives f′(x) = 36x^5. At x = 6, f′(6) = 279936.
2. For f(x) = 9x^2, find f′(4).
72
The power rule gives f′(x) = 18x^1. At x = 4, f′(4) = 72.
3. For f(x) = 11x^6, find f′(9).
3897234
The power rule gives f′(x) = 66x^5. At x = 9, f′(9) = 3897234.
4. For f(x) = 4x^4, find f′(4).
1024
The power rule gives f′(x) = 16x^3. At x = 4, f′(4) = 1024.
5. For f(x) = 4x^3, find f′(7).
588
The power rule gives f′(x) = 12x^2. At x = 7, f′(7) = 588.
6. For f(x) = 11x^3, find f′(4).
528
The power rule gives f′(x) = 33x^2. At x = 4, f′(4) = 528.
7. For f(x) = 11x^6, find f′(8).
2162688
The power rule gives f′(x) = 66x^5. At x = 8, f′(8) = 2162688.
8. For f(x) = 9x^5, find f′(5).
28125
The power rule gives f′(x) = 45x^4. At x = 5, f′(5) = 28125.
9. For f(x) = 6x^5, find f′(3).
2430
The power rule gives f′(x) = 30x^4. At x = 3, f′(3) = 2430.
10. For f(x) = 9x^4, find f′(9).
26244
The power rule gives f′(x) = 36x^3. At x = 9, f′(9) = 26244.
11. For f(x) = 12x^2, find f′(8).
192
The power rule gives f′(x) = 24x^1. At x = 8, f′(8) = 192.
12. For f(x) = 10x^6, find f′(2).
1920
The power rule gives f′(x) = 60x^5. At x = 2, f′(2) = 1920.

12 questions · Seed 104731 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 104731 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 6x^6, find f′(6).
279936
The power rule gives f′(x) = 36x^5. At x = 6, f′(6) = 279936.
2. For f(x) = 9x^2, find f′(4).
72
The power rule gives f′(x) = 18x^1. At x = 4, f′(4) = 72.
3. For f(x) = 11x^6, find f′(9).
3897234
The power rule gives f′(x) = 66x^5. At x = 9, f′(9) = 3897234.
4. For f(x) = 4x^4, find f′(4).
1024
The power rule gives f′(x) = 16x^3. At x = 4, f′(4) = 1024.
5. For f(x) = 4x^3, find f′(7).
588
The power rule gives f′(x) = 12x^2. At x = 7, f′(7) = 588.
6. For f(x) = 11x^3, find f′(4).
528
The power rule gives f′(x) = 33x^2. At x = 4, f′(4) = 528.
7. For f(x) = 11x^6, find f′(8).
2162688
The power rule gives f′(x) = 66x^5. At x = 8, f′(8) = 2162688.
8. For f(x) = 9x^5, find f′(5).
28125
The power rule gives f′(x) = 45x^4. At x = 5, f′(5) = 28125.
9. For f(x) = 6x^5, find f′(3).
2430
The power rule gives f′(x) = 30x^4. At x = 3, f′(3) = 2430.
10. For f(x) = 9x^4, find f′(9).
26244
The power rule gives f′(x) = 36x^3. At x = 9, f′(9) = 26244.
11. For f(x) = 12x^2, find f′(8).
192
The power rule gives f′(x) = 24x^1. At x = 8, f′(8) = 192.
12. For f(x) = 10x^6, find f′(2).
1920
The power rule gives f′(x) = 60x^5. At x = 2, f′(2) = 1920.

12 questions · Seed 104731 · Age guidance, not curriculum certification