Recall the proof of the formula $\frac{d}{dx}{x}^n=n{x}^{n-1},$ where we had to expand a binomial raised to the $n$th power. This only

makes sense when $n$ is an integer! Now we can extend the power rule to work for real numbers in general: use

logarithmic differentiation to prove that $\frac{d}{dx}{x}^r=r{x}^{r-1}$ for any real number $r.$