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\[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}
double f(double x, double n) {
        double r165656 = x;
        double r165657 = 1.0;
        double r165658 = r165656 + r165657;
        double r165659 = n;
        double r165660 = r165657 / r165659;
        double r165661 = pow(r165658, r165660);
        double r165662 = pow(r165656, r165660);
        double r165663 = r165661 - r165662;
        return r165663;
}

Reproduce

herbie shell --seed 2020014 +o rules:numerics
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  :precision binary64
  (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))