One-sided differentiability: a challenge for computer algebra systems

Abstract

Computer Algebra Systems (CASs) are extremely powerful and widely used digital tools. Focusing on differentiation, CASs include a command that computes the derivative of functions in one variable (and also the partial derivative of functions in several variables). We will focus in this article on real-valued functions of one real variable. Since CASs usually compute the derivative of real-valued functions as a whole, the value of the computed derivative at points where the left deriva-tive and the right derivative are different (that we will call conflicting points) should be something like “undefined”, although this isn’t always the case: the output could strongly differ depending on the chosen CAS. We have analysed and compared in this article how some well-known CASs behave when addressing differentiation at the conflicting points of five different functions chosen by the au-thors. Finally, the ability for calculating one-sided limits of CASs allows to directly compute the result in these cumbersome cases using the formal definition of one-sided derivative, which we have also analysed and compared for the selected CASs. Regarding teaching, this is an important issue, as it is a topic of Secondary Education and nowadays the use of CASs as an auxiliary digital tool for teaching mathematics is very common.