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.

If ${\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} }$ is a function such that ${\displaystyle f(x)=x^{r}}$, and ${\displaystyle f}$ is differentiable at ${\displaystyle x}$, then,

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