Variational analysis | Calculus of variations | Differential operators | Differential calculus | Topological vector spaces

Functional derivative

In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional (a functional in this sense is a function that acts on functions) to a change in a function on which the functional depends. In the calculus of variations, functionals are usually expressed in terms of an integral of functions, their arguments, and their derivatives. In an integral L of a functional, if a function f is varied by adding to it another function δf that is arbitrarily small, and the resulting integrand is expanded in powers of δf, the coefficient of δf in the first order term is called the functional derivative. For example, consider the functional where f ′(x) ≡ df/dx. If f is varied by adding to it a function δf, and the resulting integrand L(x, f +δf, f '+δf ′) is expanded in powers of δf, then the change in the value of J to first order in δf can be expressed as follows:where the variation in the derivative, δf ′ was rewritten as the derivative of the variation (δf) ′, and integration by parts was used. (Wikipedia).

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How to calculate partial derviatives

Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook Basic examples of how to calculate partial derivatives of functions. These kinds of problems are seen in a Calculus 2 course. In mathematics, a partial derivative of a function of several variables is its deriv

From playlist Learn Calculus 2 on Your Mobile Device / Learn Math on Your Phone!

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In this video I mention some of the basic methods used in calculating the derivative, for example the product, quotient, and chain rules.

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We give the definition of the partial derivative of a function of more than one variable. In addition, we present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

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From playlist Sect 2.7, Definition of Derivative

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From playlist Advanced Calculus / Multivariable Calculus

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This video provides an example of how to determine the derivative of a quadratic function using the limit definition of the derivative.

From playlist Introduction and Formal Definition of the Derivative

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From playlist Calculus

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From playlist Introduction and Formal Definition of the Derivative

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We use the definition of derivative to find the derivative of x^-2. For more calculus tutorials, please see my new "just calculus" channel: 👉https://www.youtube.com/justcalculus If you find my videos helpful, then consider supporting me on Patreon: 👉 https://www.patreon.com/blackpenred

From playlist Sect 2.7, Definition of Derivative

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From playlist AP Calculus AB

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From playlist AP Calculus BC

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From playlist AP Calculus BC

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From playlist MATH2018 Engineering Mathematics 2D

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From playlist Calculus: Derivatives

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From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?

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