Question

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible.

- what it means to say that y is an implicit function of x, and the meaning of implicit differentiation

Short answer

It means that the relation between $x,y$ is not described by expressing$y$in terms of$x$.

Step-by-step solution

Given Information

It is mentioned that $y$is an implicit function of$x$.

Simplification

It means that relation between $x$and $y$is not described by expressing $y$explicitly in terms of $x$.

In Implicit differentiation, we differentiate each side of the equation with two variables by treating one of the variables as a function of the other.