Archive for May, 2014

implicit function problem

From fakalin. If \(F(x, y, z)\) is a function of 3 variables, and the relation \(F(x, y, z) = 0\) defines each of the variables in terms of the other two, namely \(x = f(y, z)\), \(y = g(x, z)\), and \(z = h(x, y)\), then show that:

\(\left(\frac{\partial x}{\partial y}\right) \left(\frac{\partial y}{\partial z}\right) \left(\frac{\partial z}{\partial x}\right) = -1\).
(Read the article)