# Derivative of Implicit Functions

Implicit Function:
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, ${x^2} + {y^2} - x + y + 3 = 0$ is an implicit function, because the dependent variable $y$ cannot be expressed in terms of the independent variable $x$.

Example: Find $\frac{{dy}}{{dx}}$, if the given implicit function is ${x^2} + {y^2} = {a^2}$
We have the given implicit function

Differentiate with respect to $x$, we have

Where ${a^2}$any constant and derivative of constant function is is zero.