stylistic:tone, structural:summarization
Example 3

Often, it is difficult or impossible to solve explicitly for y, and implicit differentiation is the only feasible method of differentiation. An example is the equation

It is impossible to algebraically express y explicitly as a function of x, and therefore one cannot find dy / dx by explicit differentiation. Using the implicit method, dy / dx can be obtained by differentiating the equation to obtain

where dx / dx = 1. Factoring out dy / dx shows that

which yields the result

which is defined for