Let n be a positive integer and let r=1/n be the reciprocal. The derivative of the nth root function x^r=x^(1/n) is rx^(r-1) = 1/n * x^(1/n - 1) whenever the nth root of x is defined (and x is nonzero). One way to derive this is by the derivative of inverse formula. Another way is to write x^r=e^(r ln(x)) and use the chain rule, exponential rule, and logarithm rule.