dw For the functions w = xy + yz + xz, x=u+ 3v, y = u - 3v, and z= uv, express dw using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate dw dw and and du at the poir u,v) = dw Express dw and du as functions of u and v dv dw du dw dw and du dw Evaluate at dw du (Type an integer or a simplified fraction.) dw dv(3 Type an integer or a simplified fraction.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 63E
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Question

Express

∂w∂u

and

∂w∂v

as functions of u and v.

dw
dw
dw
dw
For the functions w = xy + yz + xz, x= u + 3v, y =u - 3v, and z= uv, express
and
dv
using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate
at the point
and
du
dv
ne
3
(u,v) =
2
dw
dw
and
du
Express
as functions of u and v.
dv
dw
%3D
du
dw
dv
dw
Evaluate
du
dw
3
-2
and
at
dv
dw
du
(Type an integer or a simplified fraction.)
dw
G-2)
( 3
dv
4'
(Type an integer or a simplified fraction.)
Transcribed Image Text:dw dw dw dw For the functions w = xy + yz + xz, x= u + 3v, y =u - 3v, and z= uv, express and dv using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate at the point and du dv ne 3 (u,v) = 2 dw dw and du Express as functions of u and v. dv dw %3D du dw dv dw Evaluate du dw 3 -2 and at dv dw du (Type an integer or a simplified fraction.) dw G-2) ( 3 dv 4' (Type an integer or a simplified fraction.)
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