So this is a problem for microeconomics, but should follow under general calculus: The point is x=(x1(p1,p2,u),x2(p1,p2,u)) where u is a constant on the function u(x1,x2). p1 is the price of x1 and p2 for x2. I'm supposed to show that (dx1/dp2)=(dx2/dp1). I've been given the info that for the second derivative of a multivariable function the order of differentation is irrelevant (df(x1,x2)/dx1dx2)=(df(x1,x2)/dx2dx1). All of the mentioned should also be the case for functions of more than two variables. I've tried to set second derivatives equal to each other, but obviously ended up with the exact same on both sides. I don't know where to go from here. Hints and tips would be much appreciated.