# Vector Chain Rule Derivative

This post categorized under Vector and posted on December 11th, 2018.

The chain rule can be used to derive some well-known differentiation rules. For example the quotient rule is a consequence of the chain rule and the product rule.To see this write the function f(x)g(x) as the product f(x) 1g(x).First apply the product rulepartial derivative. total differential. total derivative. chain rule. directional derivative. differentiation under the integral sign. leibnitzs rule.In mathematics physics and engineering a Euclidean vector (sometimes called a geometric or spatial vector oras heresimply a vector) is a geometric object that has magnitude (or graphicgth) and direction.Vectors can be added to other vectors according to vector algebra.A Euclidean vector is frequently represented by a line segment with a definite direction or graphically as an arrow

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The simple derivative of a function f with respect to a variable x is denoted either f(x) or (df)(dx) (1) often written in-line as dfdx. When derivatives are taken with respect to time they are often denoted using Newtons overdot notation for fluxions (dx)(dt)x..In the section we introduce the concept of directional derivatives. With directional derivatives we can now ask how a function is changing if we allow all the independent variables to change rather than holding all but one constant as we had to do with partial derivatives. In addition we will define the gradient vector to help with some of the notation and work here.Section 7-2 Proof of Various Derivative Properties. In this section were going to prove many of the various derivative facts formulas andor properties that we encountered in the early part of the Derivatives chapter. Not all of them will be proved here and some will only be proved for special cases but at least youll see that some of them arent just pulled out of the air.

Motivation. In this section we will develop expertise with an intuitive understanding of backpropagation which is a way of computing gradients of expressions through recursive application of chain rule. Understanding of this process and its subtleties is critical for you to understand and I recently came across an interesting paper graphicp Mapping Unparametrized Surfaces on the GPU by Morten Mikkelsen of Naughty Dog. This paper describes an alternative method to normal mapping closely related to graphicp mapping. The alluring prospect of this technique is that it doesnt require that a tangent graphice be defined.index click on a letter A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A to Z index index subject areas numbers & symbolsCreate your own math worksheets. Linear Algebra Introduction to matrices Matrix multiplication (part 1) Matrix multiplication (part 2)

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