The present research is a study about function approximations using derivation methods, since,
during the teaching of calculus, we come across several functions with complex formulas that
become problematic because they need more attention. Therefore, we aim to review essential
concepts of calculus such as limit and tangent line, with a view to understanding the concept and
the use of the derivative of a function to find expressions and approximate values of these functions
in certain values. The methodology adopted is based on a fully bibliographic quantitative
research, reviewing books, academic articles and lecture notes. It was found that the concepts
of differentials can be developed in order to find approximate values of roots that strongly resemble
their real values. In parallel, it is seen that the derivative of a function at a given point
brings arbitrarily good estimates, and that the smaller the chosen parameters, the smaller the
error. Furthermore, approaching the same concept, Taylor polynomials show us that an even
closer approximation of the values of a function through derivation is possible.
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