How to Use Directional Derivatives For Machine Learning: Topics of Partial Derivatives

Introduction By this point in our series on partial derivates, we not only have expanded upon the idea of multivariate equations, but also introduced the taking of partial derivatives and their associated tangent planes/linear approximations. If you have not referenced these items, we highly recommend it, for as we proceed in our application of theseContinue reading “How to Use Directional Derivatives For Machine Learning: Topics of Partial Derivatives”

Guide to Tangent Planes and Linear Approximation: Topics of Partial Derivatives

Overview Up to this point, we have really highlighted the nuts and bolts of working with partial derivatives. Firstly, it began by elaborating the roles of equations comprised of multiple variables. We extrapolate on those insights in this article. Secondly, we took a brief detour to examine the nuances of limits and continuity in theseContinue reading “Guide to Tangent Planes and Linear Approximation: Topics of Partial Derivatives”

A Guide to Partial Derivatives: Topics of Partial Derivatives

Setting the Ground on Partial Derivatives Our series which elaborates on the topic of partial derivatives began first by introducing functions of multiple variables. An understanding of how these functions operate is integral to executing partial derivatives. If you need a refresher on this subject before embarking further, check out this article. Furthermore, limits areContinue reading “A Guide to Partial Derivatives: Topics of Partial Derivatives”

Limits and Continuity Multi-Variable Functions: Topics of Partial Derivatives

Overview of Functions With Multiple Variables If you’ve been following in our blog, you may have found our discussion of vector calculus before arriving here. If not, it may prove useful to start with this topic; you may find it here. Nevertheless, limits and continuity are fundamental to conceptualizing the various aspects of calculus, andContinue reading “Limits and Continuity Multi-Variable Functions: Topics of Partial Derivatives”

Modeling Functions of Multiple Variables: Topics of Partial Derivatives

Introduction to Functions of Multiple Variables Prior to now, we have quite frequently worked with functions that relate a single variable to another variable. These functions tend to take the form: Here, f(x) represents the traditional variable y. However, in this article, we investigate higher functions that rely on relationships between multiple variable inputs. WeContinue reading “Modeling Functions of Multiple Variables: Topics of Partial Derivatives”