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

12 questions · Seed 42 · 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) = 5x^6, find f′(3).
7290
The power rule gives f′(x) = 30x^5. At x = 3, f′(3) = 7290.
2. For f(x) = 5x^5, find f′(4).
6400
The power rule gives f′(x) = 25x^4. At x = 4, f′(4) = 6400.
3. For f(x) = 6x^3, find f′(6).
648
The power rule gives f′(x) = 18x^2. At x = 6, f′(6) = 648.
4. For f(x) = 9x^3, find f′(5).
675
The power rule gives f′(x) = 27x^2. At x = 5, f′(5) = 675.
5. For f(x) = 11x^4, find f′(3).
1188
The power rule gives f′(x) = 44x^3. At x = 3, f′(3) = 1188.
6. For f(x) = 9x^5, find f′(4).
11520
The power rule gives f′(x) = 45x^4. At x = 4, f′(4) = 11520.
7. For f(x) = 9x^3, find f′(7).
1323
The power rule gives f′(x) = 27x^2. At x = 7, f′(7) = 1323.
8. For f(x) = 1x^6, find f′(1).
6
The power rule gives f′(x) = 6x^5. At x = 1, f′(1) = 6.
9. For f(x) = 9x^3, find f′(4).
432
The power rule gives f′(x) = 27x^2. At x = 4, f′(4) = 432.
10. For f(x) = 11x^3, find f′(8).
2112
The power rule gives f′(x) = 33x^2. At x = 8, f′(8) = 2112.
11. For f(x) = 8x^4, find f′(5).
4000
The power rule gives f′(x) = 32x^3. At x = 5, f′(5) = 4000.
12. For f(x) = 9x^6, find f′(6).
419904
The power rule gives f′(x) = 54x^5. At x = 6, f′(6) = 419904.

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

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

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. For f(x) = 5x^6, find f′(3).
7290
The power rule gives f′(x) = 30x^5. At x = 3, f′(3) = 7290.
2. For f(x) = 5x^5, find f′(4).
6400
The power rule gives f′(x) = 25x^4. At x = 4, f′(4) = 6400.
3. For f(x) = 6x^3, find f′(6).
648
The power rule gives f′(x) = 18x^2. At x = 6, f′(6) = 648.
4. For f(x) = 9x^3, find f′(5).
675
The power rule gives f′(x) = 27x^2. At x = 5, f′(5) = 675.
5. For f(x) = 11x^4, find f′(3).
1188
The power rule gives f′(x) = 44x^3. At x = 3, f′(3) = 1188.
6. For f(x) = 9x^5, find f′(4).
11520
The power rule gives f′(x) = 45x^4. At x = 4, f′(4) = 11520.
7. For f(x) = 9x^3, find f′(7).
1323
The power rule gives f′(x) = 27x^2. At x = 7, f′(7) = 1323.
8. For f(x) = 1x^6, find f′(1).
6
The power rule gives f′(x) = 6x^5. At x = 1, f′(1) = 6.
9. For f(x) = 9x^3, find f′(4).
432
The power rule gives f′(x) = 27x^2. At x = 4, f′(4) = 432.
10. For f(x) = 11x^3, find f′(8).
2112
The power rule gives f′(x) = 33x^2. At x = 8, f′(8) = 2112.
11. For f(x) = 8x^4, find f′(5).
4000
The power rule gives f′(x) = 32x^3. At x = 5, f′(5) = 4000.
12. For f(x) = 9x^6, find f′(6).
419904
The power rule gives f′(x) = 54x^5. At x = 6, f′(6) = 419904.

12 questions · Seed 42 · Age guidance, not curriculum certification