Lecturer: Filomena Soares

Polytechnic of Porto

Frequently students engaged in Math courses, they must or should attend in non-Math Bachelor degrees, have many doubts about their application/significance, questioning why some contents are relevant.  One of these issues is the concept of derivative function and its applications (and reciprocally speaking - anti-derivatives/integrals/primitive functions).
Derivatives are extremely helpful for examining "change” since, by the way they are defined, they show us the variation of one variable (dependent/function) when another one (independent) changes. Their application in economic and business contexts, when working with specific functions like revenue, cost or profit, gives derivatives a direct interpretation, relying on the "marginal” adjective, allows us to estimate how these functions are changing as the quantity produced or/and sold changes.  Another typical application of derivatives is the price elasticity of demand, where we try to conclude how changes in specific prices affect the consumers' demanded quantity.
In this small lecture we will try to look at these concepts (derivative and partial derivative) and apply them to several examples drawn from the real world problems in the economical field. Making extensive calculus, working with "difficult” expressions is important in terms of Math skills but, in the end, all these are "nonsense” if one cannot interpret the obtained particular results.