If the independent and the dependent variables are mixed up in such a way that the dependent variable cannot be expressed in terms of independent variable, then such a function is called an implicit function.
For example, is an implicit function, because the dependent variable cannot be expressed in terms of the independent variable .
Example: Find , if the given implicit function is
We have the given implicit function
Differentiate with respect to , we have
Where any constant and derivative of constant function is is zero.