**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Derivability and Composition of Functions

Description

This lecture covers the concept of derivability, focusing on the composition of functions and their derivatives. It explains the chain rule and provides examples to illustrate the application of these concepts.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

In course

MATH-101(d): Analysis I

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable.

Related concepts (176)

Parental leave

Parental leave, or family leave, is an employee benefit available in almost all countries. The term "parental leave" may include maternity, paternity, and adoption leave; or may be used distinctively from "maternity leave" and "paternity leave" to describe separate family leave available to either parent to care for small children. In some countries and jurisdictions, "family leave" also includes leave provided to care for ill family members. Often, the minimum benefits and eligibility requirements are stipulated by law.

Chain rule

In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely, if is the function such that for every x, then the chain rule is, in Lagrange's notation, or, equivalently, The chain rule may also be expressed in Leibniz's notation. If a variable z depends on the variable y, which itself depends on the variable x (that is, y and z are dependent variables), then z depends on x as well, via the intermediate variable y.

Definition

A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.

Lexical definition

The lexical definition of a term, also known as the dictionary definition, is the definition closely matching the meaning of the term in common usage. As its other name implies, this is the sort of definition one is likely to find in the dictionary. A lexical definition is usually the type expected from a request for definition, and it is generally expected that such a definition will be stated as simply as possible in order to convey information to the widest audience.

Circular definition

A circular definition is a type of definition that uses the term(s) being defined as part of the description or assumes that the term(s) being described are already known. There are several kinds of circular definition, and several ways of characterising the term: pragmatic, lexicographic and linguistic. Circular definitions are related to Circular reasoning in that they both involve a self-referential approach. Circular definitions may be unhelpful if the audience must either already know the meaning of the key term, or if the term to be defined is used in the definition itself.

Related lectures (1,000)

Derivability and DifferentiabilityMATH-101(g): Analysis I

Covers derivability, differentiability, rules of differentiation, and the relationship between differentiability and continuity.

Derivability and Chain RuleMATH-101(d): Analysis I

Covers the demonstration of the chain rule and the theorem of Rolle.

Limits and ExamplesMATH-101(d): Analysis I

Explores the concept of limits and provides examples of their existence and non-existence in various functions.

Derivatives of Composite FunctionsMATH-101(d): Analysis I

Covers derivatives of composite functions and the chain rule in calculus.

Derivative of a Function: Tangent Equation

Explores finding tangent equations and slopes through derivatives.