Chapter 3.7, Problem 50E

Power rule for rational exponents Let $p$ and $q$ be integers with $q>0$. If $y=x^{p/q}$, differentiate the equivalent equation $y^q=x^p$ implicitly and show that, for $y\ne 0$, $\frac{d}{dx}{x}^{p/q}=\frac{p}{q}{x}^{\left(p/q\right)-1}$.