A computational point of view on teaching derivatives

The strong connection between mathematics and informatics highlights the important role of scientific computing in many applications. Unfortunately, is traditionally taught without investigating possible connections abstract problem solving use algorithms capable being implemented on a computer. Since mathematical theory practice are separately, students fail to appreciate utility mathematics. In this paper, we briefly explain how typical lecture obtaining derivatives differential calculus can benefit from examples high-level languages like MATLAB, Python or R. Such help guide better understanding theoretical concepts limits finite precision floating-point arithmetic. We argue that, while historical findings Leibniz Newton good starting points for introducing difference approximation methods, does not preclude new approaches numerically using Infinite Computer Arithmetic.