# Power rule

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.