Power rule

Part of a series of articles about
Calculus
${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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Miscellanea Precalculus History Glossary List of topics Integration Bee Mathematical analysis Nonstandard analysis
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In calculus, the power rule is used to differentiate functions of the form ${\displaystyle f(x)=x^{r}}$, whenever ${\displaystyle r}$ is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rule underlies the Taylor series as it relates a power series with a function's derivatives.