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The implicit-function

  1. Nov 26, 2007 #1
    1. The problem statement, all variables and given/known data

    Assuming that the equation F(U, x1, x2, ..., xn) = 0 implicity defines a utility function U=f(x1, x2, ..., xn):

    Find the expressions for [tex]\partial[/tex]U/[tex]\partial[/tex]x2, [tex]\partial[/tex]U/[tex]\partial[/tex]xn, [tex]\partial[/tex]x3/[tex]\partial[/tex]x2, and [tex]\partial[/tex]x4/[tex]\partial[/tex]xn.

    2. Relevant equations

    3. The attempt at a solution

    I read the textbook to solve this problem but still cannot figure out how to solve it.
    Please help me.
  2. jcsd
  3. Nov 26, 2007 #2

    Ben Niehoff

    User Avatar
    Science Advisor
    Gold Member

    If U is some function [itex]U(\vec x)[/itex], then what is

    [tex]\frac{\partial F(U;\vec x)}{\partial x_2}[/tex]


    Hint: Apply the chain rule.
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