Let f be a function with continuous second derivatives, defined by: 2 = f(r° + y°, 2ry) If we take "= 1 + and w = 2ry we obtain *= 2rfu + 2yf« and v= 2yfu +2rfw, then A) 2 fu + 2r fau + 2fw + 2yfuw %3D B) 4r° fuu + 8ry fuw + 4y° fww C) 4r° fuu + 4ryfy + 4y fww +4ryfwu

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 18E
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Let f be a function with continuous second derivatives, defined by:
2 = f(2° + y°, 2ry)
If we take
u =2+y and w=
2ry we obtain % = 2rfu +2yfw and y = 2y fu + 2r fw, then:
A)
= 2fu + 2r fuu + 2fw + 2y fuw
B)
4x fuu + 8ry fuw + 4y² fww
%3D
4x fau + 4ry fuw + 4y° Sww + 4ryfwu
D)
2fu + 4x? fuu + 8ry fuw + 4y fww
Transcribed Image Text:Let f be a function with continuous second derivatives, defined by: 2 = f(2° + y°, 2ry) If we take u =2+y and w= 2ry we obtain % = 2rfu +2yfw and y = 2y fu + 2r fw, then: A) = 2fu + 2r fuu + 2fw + 2y fuw B) 4x fuu + 8ry fuw + 4y² fww %3D 4x fau + 4ry fuw + 4y° Sww + 4ryfwu D) 2fu + 4x? fuu + 8ry fuw + 4y fww
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