If the independent and the dependent variables are mixed up in such a way that the dependent variable cannot be expressed in terms of the independent variable, this 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
Differentiating with respect to , we have
Here, any constant and the derivative of the constant function is zero.