Power Rule
The power rule is the workhorse of polynomial calculus. Integration reverses it, except n = −1 which produces a logarithm.
Variables
- n — A real exponent. Integration needs n ≠ −1.
When to use it
Polynomials, monomials, and any term you can rewrite as a power of x.
Worked example
d/dx x^4
- 4x^3
Answer: 4x³
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Example problems
Common mistakes
Integrating x⁻¹ with the power rule
∫ x⁻¹ dx = ln|x| + C, not x⁰/0.
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Frequently asked questions
Does the power rule work for square roots?
Yes. √x = x^{1/2}, so the derivative is (1/2)x^{−1/2}.