Mathematical Foundations · Differential Calculus

Differential Calculus: Derivative and Differentiability

Public introduction · full guide in Eikos

Introduction

What this guide covers

A rigorous exposition on instantaneous variation, the topological properties of differentiable functions and the transition towards calculus in multiple dimensions.

Overview

Topics covered

  • Introduction
  • Derivative and Differentiability
  • Introduction and Historical-Philosophical Context
  • Historical Evolution
  • The Crisis of Infinitesimals and Nineteenth-Century Rigor
  • The Formal Definition of Derivative

Related concepts

Main connections

  • Calculus & differentiation
  • Linear algebra & matrices
  • Supervised machine learning
  • Binomial distribution
  • Metric definition & evaluation

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

f'(c)=limx→cf(x)−f(c)x−c
View LaTeX sourcef'(c) = \lim_{x \to c} \frac{f(x) - f(c)}{x - c}