This work presents the derivatives of functions of several variables and highlights their appli-
cations. Its main objective is to present two applications, namely, related rates and function
approximations, and seeking to determine a generalization of the derivation for more general
functions. For this, the fundamental concepts of differential calculus are presented and vari-
ous types of problems related to related rates are exposed, as well as a notion of derivation of
functions of several variables, which here are linear transformations and, extends, in a certain
sense, the notion of derivative for functions of one variable. The methodology used in this mo-
nograph is exploratory, bibliographical, and the approach is qualitative. The results allowed us
to create an appendix containing a diagram that shows a general algorithm for solving problems
involving related rates, since most cases follow the same resolution process, which makes the
development of an “algorithm” possible. As a result, this research shows that derivatives make
it possible to find good approximations of the image of a function around a point.
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