## 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:

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