Implicit and explicit equations

In mathematics, an implicit equation is a relation of the form R(x₁, …, x_n) = 0, where R is a function of several variables. For example, the implicit equation of the unit circle is x² + y² − 1 = 0. An explicit equation, on the other hand, expresses one variable in terms of one or more others. For example, y = x² + x − 1 is a function that expresses the variable y in terms of x.

Resources

• Differentiating Implicit and Explicit Functions, Math Mutts
• Implicit Differentiation, Openstax