Mathematics · Grades 11–12
Power-rule derivatives
Multiply by the exponent and reduce that exponent by one. These tasks use positive integer powers.
The key idea
Multiply by the exponent and reduce that exponent by one. These tasks use positive integer powers.
d(axⁿ)/dx = an xⁿ⁻¹
Worked examples
For f(x) = 7x^2, find f′(3).
f′(x) = 14x^1; f′(3) = 42
42
For f(x) = 4x^5, find f′(4).
f′(x) = 20x^4; f′(4) = 5120
5120
Try it yourself
For f(x) = 8x^4, find f′(3).
For f(x) = 3x^4, find f′(1).
Check your understanding
Answers and marking notes
- 864
f′(x) = 32x^3; f′(3) = 864
- 12
f′(x) = 12x^3; f′(1) = 12
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.