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dw dw In each of the following, find and dr’ ds using the Chain Rule. 1. w = ry + yz +az; x = r+s+t; y = rst; 2 = r² + s² + t²

dw dw In each of the following, find and dr’ ds using the Chain Rule. 1. w = ry + yz +az; x = r+s+t; y = rst; 2 = r² + s² + t²

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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dw dw In each of the following, find and Ət ar' əs using the Chain Rule. 1. w = ry + yz + 2z; x = r+s+t; y = rst; 2 = r² + s² +²
Transcribed Image Text:dw dw In each of the following, find and Ət ar' əs using the Chain Rule. 1. w = ry + yz + 2z; x = r+s+t; y = rst; 2 = r² + s² +²
The Chain Rule for Partial Derivative Theorem (Chain Rule) Let u = f(x, y) be a differentiable function Əx dx dy dr' ds' dr dy and ds of x and y, where x = F(r, s) and y = G(r, s). Suppose all exists. Then u is a function of r and s and du + dr %3D dr dx dy dr and ди ds 16 (Generalized Chain Rule) Let w = f(x1,"2,.…. .,,) be a differentiable function of æ1, 12, ... Ln, where T; = F4(91; Y2, … . ym), 1< Theorem %3D k < n. Suppose for all 1 < k < n, , 1<ism exist. Then w is a W function of x1, X2, ... I, and for all 1 sism Σ %3D k=1 II ||
Transcribed Image Text:The Chain Rule for Partial Derivative Theorem (Chain Rule) Let u = f(x, y) be a differentiable function Əx dx dy dr' ds' dr dy and ds of x and y, where x = F(r, s) and y = G(r, s). Suppose all exists. Then u is a function of r and s and du + dr %3D dr dx dy dr and ди ds 16 (Generalized Chain Rule) Let w = f(x1,"2,.…. .,,) be a differentiable function of æ1, 12, ... Ln, where T; = F4(91; Y2, … . ym), 1< Theorem %3D k < n. Suppose for all 1 < k < n, , 1<ism exist. Then w is a W function of x1, X2, ... I, and for all 1 sism Σ %3D k=1 II ||
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