Power Rule (Derivatives)

Derivative of a power of x.

\frac{d}{d x} x^{n} = n x^{n - 1}

Variables

n: Any real exponent

Explanation

Bring the exponent down as a coefficient and reduce the exponent by one. It works for negative and fractional exponents too, e.g. $\frac{d}{d x} x = \frac{1}{2 x}$ .

Example

$\frac{d}{d x} (4 x^{3}) = 12 x^{2}$ .

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Differentiate functions step by step using the power, product, quotient and chain rules. Supports higher-order and partial derivatives.

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Related formulas

Product Rule

Derivative of a product of two functions.

Chain Rule

Derivative of a composite function.