AP Calculus AB and BC glossary
Implicit function
An implicit function is one defined by an equation relating the variables without the output isolated, such as the equation of a circle. Its derivative is found by differentiating both sides and solving for the derivative rather than by rearranging first.
Many implicit equations do not define a single function at all. A circle fails the vertical line test, yet it still has a well-defined tangent slope at almost every point, which is what implicit differentiation computes.
The resulting derivative usually depends on both variables, so evaluating it requires a full point rather than just an value.
Appears in: Unit 3: Chain Rule, Implicit, and Inverses