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z = f(a + y, 2ry) f we take u = x' + y' and w = 2xy we obtain z, = 2xf, + 2yf, and z, = 2yf, + 2xf., then: A) dyðx = 2 fu + 4ry fuu +(4x + 4y²) fuw + 2fw + 4ryfww B) = 4.ry fuu + 4.x fuw + 4y fwu + 4.ryfww дудх C) = 4ry fuu + (4x + 4y*) fuw + 2fw + 4ry fww D) dydr = 2x fuu + 2fw + 2yfww %3D

z = f(a + y, 2ry) f we take u = x' + y' and w = 2xy we obtain z, = 2xf, + 2yf, and z, = 2yf, + 2xf., then: A) dyðx = 2 fu + 4ry fuu +(4x + 4y²) fuw + 2fw + 4ryfww B) = 4.ry fuu + 4.x fuw + 4y fwu + 4.ryfww дудх C) = 4ry fuu + (4x + 4y*) fuw + 2fw + 4ry fww D) dydr = 2x fuu + 2fw + 2yfww %3D

College Algebra (MindTap Course List)
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 17E: Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.
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Let f be a function with continuous second derivatives, defined by: z = f(2? + y, 2xy) If we take u = x + y' and w = 2xy we obtain z, = 2xf, + 2yf, and z, = 2yf, + 2xfu , then: %3D A) дудх 2 fu + 4.xy fuu + (4.x² + 4y°)fuw + 2 fw + 4xy fww B) = 4xy fuu + 4x fuw + 4y? fwu + 4.xyfww C) dydx = 4.ry fuu + (4x2 + 4y?) fuw + 2fw + 4.ry fww D) дудл 2.x fuu + 2fw + 2y fww
Transcribed Image Text:Let f be a function with continuous second derivatives, defined by: z = f(2? + y, 2xy) If we take u = x + y' and w = 2xy we obtain z, = 2xf, + 2yf, and z, = 2yf, + 2xfu , then: %3D A) дудх 2 fu + 4.xy fuu + (4.x² + 4y°)fuw + 2 fw + 4xy fww B) = 4xy fuu + 4x fuw + 4y? fwu + 4.xyfww C) dydx = 4.ry fuu + (4x2 + 4y?) fuw + 2fw + 4.ry fww D) дудл 2.x fuu + 2fw + 2y fww
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