Smooth functions | Differential calculus | Multivariable calculus
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cusp. If x0 is an interior point in the domain of a function f, then f is said to be differentiable at x0 if the derivative exists. In other words, the graph of f has a non-vertical tangent line at the point (x0, f(x0)). f is said to be differentiable on U if it is differentiable at every point of U. f is said to be continuously differentiable if its derivative is also a continuous function over the domain of the function . Generally speaking, f is said to be of class if its first derivatives exist and are continuous over the domain of the function . (Wikipedia).
Differentiability of a function - an example
Free ebook http://tinyurl.com/EngMathYT A simple example of how to determine when a function is differentiable. Such ideas are seen in university mathematics.
From playlist A first course in university mathematics
If a function is differentiable then it is continuous
👉 Learn how to determine the differentiability of a function. A function is said to be differentiable if the derivative exists at each point in its domain. To check the differentiability of a function, we first check that the function is continuous at every point in the domain. A function
From playlist Find the Differentiability of a Function
How to determine the points that make the function differentiable
👉 Learn how to determine the differentiability of a function. A function is said to be differentiable if the derivative exists at each point in its domain. To check the differentiability of a function, we first check that the function is continuous at every point in the domain. A function
From playlist Find the Differentiability of a Function
Learn to find the value that makes the piecewise function differentiable and continuous
👉 Learn how to determine the differentiability of a function. A function is said to be differentiable if the derivative exists at each point in its domain. To check the differentiability of a function, we first check that the function is continuous at every point in the domain. A function
From playlist Find the Differentiability of a Function
When is a curve differentiable?
► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course 0:00 // What is the definition of differentiability? 0:29 // Is a curve differentiable where it’s discontinuous? 1:31 // Differentiability implies continuity 2:12 // Continuity doesn
From playlist Popular Questions
Values b and c that make the piece wise function differentiable
👉 Learn how to determine the differentiability of a function. A function is said to be differentiable if the derivative exists at each point in its domain. To check the differentiability of a function, we first check that the function is continuous at every point in the domain. A function
From playlist Find the Differentiability of a Function
Multivariable Calculus | Differentiability
We give the definition of differentiability for a multivariable function and provide a few examples. http://www.michael-penn.net https://www.researchgate.net/profile/Michael_Penn5 http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
Definition of Differentiability
Discussion of definition of differentiability, focussing on hybrid (piecewise) functions.
From playlist Further Calculus - MAM Unit 3
How to determine the points of differentiability
👉 Learn how to determine the differentiability of a function. A function is said to be differentiable if the derivative exists at each point in its domain. To check the differentiability of a function, we first check that the function is continuous at every point in the domain. A function
From playlist Find the Differentiability of a Function
What are Exact Differential Equations (Differential Equations 28)
https://www.patreon.com/ProfessorLeonard An explanation of the origin, use, and solving of Exact Differential Equations
From playlist Differential Equations
KS5 - Product, Quotient & Chain Rules
"Product, quotient and chain rules."
From playlist Differentiation (A2/Advanced)
Matthijs Vákár: Mathematical foundations of automatic differentiation
HYBRID EVENT Recorded during the meeting "Logic of Probabilistic Programming" the January 31, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Aud
From playlist Virtual Conference
Rules of differentiation -- Calculus I
This lecture is on Calculus I. It follows Part I of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus I
This video defines differentials, finds differentials of functions, uses differential to estimate a function value, and find propagated and relative error. http://mathispower4u.com
From playlist Differentiation Application - Differentials and Tangent Line Approximations
Continuity and Differentiability
This calculus video tutorial provides a basic introduction into continuity and differentiability. Continuity tells you if the function f(x) is continuous or discontinuous at some point in the interval (a,b). Points of discontinuity include holes, jump discontinuities, and infinite discon
From playlist New Calculus Video Playlist
Introduction to Exact Differential Equations
Introduction to Exact Differential Equations This video goes through all of the theory of exact differential equations and explains how and why the solution process works. Two different solution techniques are given as well. I hope you enjoy this video:)
From playlist Differential Equations
Progress in Symbolic Differential Equations
During this talk I will give an overview of recent developments, new features and improvements in Wolfram Language related to symbolic solutions of ordinary differential equations. I will begin by speaking about the recently introduced DSolve option IncludeSingularSolutions, which allows o
From playlist Wolfram Technology Conference 2022
Find the values a and b that make the function differentiable
👉 Learn how to determine the differentiability of a function. A function is said to be differentiable if the derivative exists at each point in its domain. To check the differentiability of a function, we first check that the function is continuous at every point in the domain. A function
From playlist Find the Differentiability of a Function