Exercise 7.5.1 (i) Show carefully that the derivative of g(x) = arcsin(x) is given by g' (2) = V1 - 22 (ii) Consider the non-bijective function f : R - R defined by f (x) = sin(x). 27T Find a local inverse for f at To = 3 Hint: The function arcsin is not a local inverse of sin at To = 3