Example 3

Given x² - 2y² = 4, y ≤ 0, find dy/dx.

Solving the original equation for y, we get

Thus dy/dx in terms of x is

The graph of this function is shown in Figure 2.8.2.

Implicit differentiation can even be applied to an equation that does not by itself determine y as a function x. Sometimes extra inequalities must be assumed in order to make y a function of x.