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Example 3

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

02_differentiation-484.gif

Solving the original equation for y, we get

02_differentiation-485.gif

Thus dy/dx in terms of x is

02_differentiation-486.gif

The graph of this function is shown in Figure 2.8.2.

02_differentiation-487.gif

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.


Last Update: 2006-11-15