Understanding Leibniz Notation in Calculus: Formal and Informal Interpretations

This article is an educational guide explaining Leibniz notation in calculus, written by the author to help themselves and others understand this mathematical notation system. The article explores the formal and informal interpretations of Leibniz notation (dy/dx), discusses its ambiguities and vagaries as noted by mathematician Spivak, and compares it with Lagrange notation. It serves as a tutorial for those already familiar with the definition of derivative and Lagrange notation, aiming to clarify the proper understanding and usage of Leibniz notation in mathematics.