Implicit Differentiation

So far, we have been working with only one kind of function defined by a general rule of correspondence . These are called explicit functions. We will now see another kind of functions called implicit functions. An implicit function is that function which can be defined by the general equation .

Note that implicit functions cannot sometimes be put in the form a single explicit function. That means that it cannot be solved for one variable in terms of another.

Example

A function is defined implicitly by the equation . Find .

Solution

Example

Find the derivative of the implicit function  at x=3.

Solution