The Power Rule for Derivatives

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

Worked examples

Differentiate term by term.

$12 x^{3} - 10 x$ . The constant 7 has a derivative of 0.

Rewrite: $x^{1/2}$

$\frac{1}{2} x^{- 1/2} = \frac{1}{2 x}$

Rewrite: $x^{- 2}$

$- 2 x^{- 3} = - \frac{2}{x ^{3}}$

$\frac{d}{d x} (5) = 5$

A constant doesn't change, so its slope is 0. Its derivative is 0. The power rule is for powers of $x$ .

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