An implicit function is a function that is defined implicitly by a relation between its argument and its value.
If the left hand side of the equation
For most implicit functions, there is no formula which defines them explicitly. However, various numerical methods exist for computing approximately the value of
Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions.
Previously, the functions we have investigated were explicit functions of one variable with respect to another.
Therefore:
As
For example, given the expression
Solving for
A circle can be described by the equation
where
and you can now find the slope at any point
Path of a Point on a Circle
The path of a point on a circle can only be expressed as an implicit function.