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6 results for “power rule”

Formulae (6)

\log_b(x^n) = n \cdot \log_b(x)

The logarithm of a power equals the exponent times the logarithm.

\log_b(x^n) = n\log_b x

The log of a power brings the exponent to the front.

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

Derivative of a power function.

\int x^n\,dx = \frac{x^{n+1}}{n+1} + C, \; n \ne -1

Antiderivative of a power function.

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

Derivative of a power function.

\int x^n\,dx = \frac{x^{n+1}}{n+1} + C

Antiderivative of a power function (n≠-1).