1)Show that, for each natural number n, the function f_n(x) = x^(1/n) has derivative f_n ' (x) = 1/n x ^ (1/n - 1) for x not equal to 0.
2)Show that, for each real number b>0, the function f(x) = b^x (defined by b^x = sup{b^r, r rational, r<=x}) is differentiable for all real x, with f'(x) = C b^x for some constant C (no need to compute this constant exactly).