Implicit Utility Function Equations: Solving for Partial Derivatives

[christine1986]

Homework Statement

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

Find the expressions for $$\partial$$U/$$\partial$$x2, $$\partial$$U/$$\partial$$xn, $$\partial$$x3/$$\partial$$x2, and $$\partial$$x4/$$\partial$$xn.

Homework Equations

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.

 

[Ben Niehoff]

If U is some function $U(\vec x)$, then what is

$$\frac{\partial F(U;\vec x)}{\partial x_2}$$

?

Hint: Apply the chain rule.