# 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 the independent variable, this 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

Differentiating with respect to $x$, we have

Here, ${a^2}$ any constant and the derivative of the constant function is zero.