Verify that the conclusion of Clairaut's theorem holds, that is, Uxy = Uyx" u = x5y8 - y5 With u = x5y8y5, we have the following. 5x4 U xy = Uyx = "y=40x4₂7 40x¹y7 = 8x5y7 - 5y4 × Since u xy X = U Clairaut's theorem holds for u = x5y8-y5. 'yx'

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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Verify that the conclusion of Clairaut's theorem holds, that is, uxy = U.
"yx'
u = x5y8 - y5
With u = x
=
"y =
Uy
x5y8 - y5, we have the following.
=
Since u
4
5x
8x5y7 - 5y4x
Uyx 40x4y7
40x4y7
xy
X
x5y8 - y5.
= U Clairaut's theorem holds for u = x
"yx'
Transcribed Image Text:Verify that the conclusion of Clairaut's theorem holds, that is, uxy = U. "yx' u = x5y8 - y5 With u = x = "y = Uy x5y8 - y5, we have the following. = Since u 4 5x 8x5y7 - 5y4x Uyx 40x4y7 40x4y7 xy X x5y8 - y5. = U Clairaut's theorem holds for u = x "yx'
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