La derivada en varias variables como analog\'ia formal de su hom\'onima escalar

TL;DR

This paper explores formal analogies between single-variable and multivariable differential calculus, introducing derivability in multiple variables through the concept of secant planes and their limit behavior.

Contribution

It presents a novel approach to understanding multivariable derivability by extending the single-variable concept via secant plane limits.

Findings

Established a formal analogy between single and multivariable derivatives.

Introduced a method to study multivariable derivability using secant planes.

Provided insights into the geometric interpretation of derivatives in multiple variables.

Abstract

Some formal analogies between the Differential Calculus in One Variable and the Differential Calculus in Several Variables are presented. It is studied and introduced the derivability of functions at several variables from the single variable conceptual analogous. This is obtained from exploring the dynamic image of limit of a family of slopes of secants planes to the graphic of a bivariate function.