Articles containing proofs | Theorems in analysis | Theorems in calculus | Multivariable calculus
The triple product rule, known variously as the cyclic chain rule, cyclic relation, cyclical rule or Euler's chain rule, is a formula which relates partial derivatives of three interdependent variables. The rule finds application in thermodynamics, where frequently three variables can be related by a function of the form f(x, y, z) = 0, so each variable is given as an implicit function of the other two variables. For example, an equation of state for a fluid relates temperature, pressure, and volume in this manner. The triple product rule for such interrelated variables x, y, and z comes from using a reciprocity relation on the result of the implicit function theorem, and is given by where each factor is a partial derivative of the variable in the numerator, considered to be a function of the other two. The advantage of the triple product rule is that by rearranging terms, one can derive a number of substitution identities which allow one to replace partial derivatives which are difficult to analytically evaluate, experimentally measure, or integrate with quotients of partial derivatives which are easier to work with. For example, Various other forms of the rule are present in the literature; these can be derived by permuting the variables {x, y, z}. (Wikipedia).
Triple product rule | Lecture 15 | Vector Calculus for Engineers
Derivation of the reciprocity relation and the triple product rule. The reciprocity relation is sometimes called the reciprocal theorem, and the triple product rule is sometimes called the reciprocity theorem. The triple product rule is also sometimes called the cyclic chain rule, cyclic
From playlist Vector Calculus for Engineers
The Product Rule of Differentiation (Introduction)
This video is a new version of the introductory video to the product rule of differentiation. Site: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Differentiation Using the Product Rule
Triple product rule: the ideal gas law | Lecture 16 | Vector Calculus for Engineers
Demonstration of the triple product rule (also known as the cyclic chain rule, cyclic relation, cyclical rule or Euler's chain rule) for the ideal gas law. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture notes at http://www.math.ust.hk/~machas/vector
From playlist Vector Calculus for Engineers
Product Rule (1 of 2: It's Complicated...)
More resources available at www.misterwootube.com
From playlist Introduction to Differentiation
Ex 1: Determine a Derivative Using the Product Rule Involving a Trig Function
This video provides an example of determining a derivative using the product rule involving a trigonometric function. Complete Video List at http://www.mathispower4u.com
From playlist Differentiation Using the Product Rule
What does a triple integral represent?
► My Multiple Integrals course: https://www.kristakingmath.com/multiple-integrals-course Skip to section: 0:15 // Recap of what the double integral represents 1:22 // The triple integral has two uses (volume and mass) 1:45 // How to use the triple integral to find volume 8:59 // Why the
From playlist Calculus III
Proof of the Dot Product Theorem
Dot products are essential in a mathematician's toolbox. There is a property of dot products, however, that is often taken for granted: the multiplication of the magnitudes of two vectors by the cosine of the angle between them equals the sum of the multiplication of their respective compo
From playlist Fun
Multivariable Calculus: Cross Product
In this video we explore how to compute the cross product of two vectors using determinants.
From playlist Multivariable Calculus
The vector cross-product is another form of vector multiplication and results in another vector. In this tutorial I show you a simple way of calculating the cross product of two vectors.
From playlist Introducing linear algebra
Derivative of a Triple Product
Derivatives of triple products work similar to regular product rules! Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. T
From playlist Calc 1
Taylor Series Solutions to Initial Value Problems - 2nd Order
This video explains how to determine a Taylor series solution to an initial value problem. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Here are the URL's (both versions) for today's 5 GAS (Genuinely Approachable Sudoku) puzzles: GAS 401 – Seminonconsecutive by Clover: https://tinyurl.com/4kpe7hf8 https://f-puzzles.com/?id=2b58mf9o Normal sudoku rules apply. Some rows and columns are marked with '0'. Within these rows and
From playlist All the GAS - Genuinely Approachable Sudokus
Introduction to Triple Scalar Product (SoME2, 3b1b)
We introduce the triple scalar product and discuss the volume of a parallelepiped. Knowledge of scalar product and vector product of two vectors is assumed. This is a submission for Summer of Math Exposition SoME2 from 3blue1brown. 00:00 Introduction 02:00 Example on computation 03:52 M
From playlist Summer of Math Exposition 2 videos
Walter van Suijlekom: Non-commutative geometry and spectral triples - Lecture 2
Mini course of the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: Our starting point is a spectral approach to geometry, starting with the simple ques tion ’can one hear the shape of a drum’. This was phrased by Mark Kac in t
From playlist Noncommutative geometry meets topological recursion 2021
Here's where you can try today's five GAS (Genuinely Approachable Sudoku) puzzles: GAS 291 – Hi Mark! by Philip: https://tinyurl.com/3dj8r73y Normal sudoku rules apply. Digits in corner circles must appear in the surrounding four cells, in some order. Digits in cells separated by a V must
From playlist All the GAS - Genuinely Approachable Sudokus
Hydrohalogenation of alkynes | Alkenes and Alkynes | Organic chemistry | Khan Academy
Reaction of an alkyne with a hydrogen halide, leading to formation of a halogenated alkene or alkane. Created by Jay. Watch the next lesson: https://www.khanacademy.org/science/organic-chemistry/alkenes-alkynes/alkyne-reactions/v/hydration-of-alkynes?utm_source=YT&utm_medium=Desc&utm_camp
From playlist Alkenes and alkynes | Organic Chemistry | Khan Academy
Calculus 3.07e - The Product Rule
The Product Rule for derivatives
From playlist Calculus Ch 3 - Derivatives
Geometric Algebra - Duality and the Cross Product
In this video, we will introduce the concept of duality, involving a multiplication by the pseudoscalar. We will observe the geometric meaning of duality and also see that the cross product and wedge product are dual to one another, which means that the cross product is already contained w
From playlist Geometric Algebra