Use the chain rule to find the derivative of: 1. f (ac) = ex S P 2. f (a) = (In (a) )2Claim: the utility functions 11,1; R2 I> R defined by u(a., b) = a1/3b2/3 and 'u(a., b) = 0.264 represent the same preferences. This means that the relative utility tradeo of infinitesimal changes in a consumption bundle, as represented by the slope of the indifference curve at a point (a, b) E R2 , is the same for both utility functions. Use the implicit function theorem to prove the claim. Suppose that c > 0, and that u(a., b) 2 aszc, and suppose that we treat a. as a function (1(1)) that holds utility constant for given values of (1. Calculate da/db at any pair ((1,5). :Im