Let u=u(x, y), where x=x(s, t) and y=y(s,t) and assume that these functions have con- tinuous second partials. Show that d’u_ d*u (dx)2 du dxdy , du ds2 dx² \as du dx dx ds² du d²y +2- дхду дs дs ду? (дs dy ds²

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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Let u=u(x, y), where x=x(s, 1) and y=y(s,t) and assume that these functions have con-
tinuous second partials. Show that
d²u_ du (dx
ds2
д'и дх ду , д'и (ду
ди д'x , ди д'у
+2-
ds
дхду дs дs
dy² ds
dx ds?
dy ds²
Transcribed Image Text:Let u=u(x, y), where x=x(s, 1) and y=y(s,t) and assume that these functions have con- tinuous second partials. Show that d²u_ du (dx ds2 д'и дх ду , д'и (ду ди д'x , ди д'у +2- ds дхду дs дs dy² ds dx ds? dy ds²
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