Find the Partial Derivatives of the functions with respect to each variable15) f(x,y) =X+y-1Ans. fx--1(x+ y}²• I, =(x+y}%3D%3D-у' -1(y-1)2 ]yAns f = e*y»1), f, = elx-y•1)X+y-x -16) f(x,y) =-ху —1Ans. fx=%3D%3D(xy-1)²) f(x,y) = elx*»y«1)118) f(x, y) = In(x+y)Ans. f=fy%3D%3DX+yX+y9) f(x,y)=sin (x-3y)Ans. f = 2 sin(x- 3y) cos(x- 3y),fy =-6sin(x- 3y) cos(x- 3y)10) f(x,y) = x"Ans f = yx"1, fy, = x' In(x)11) f(x,y)= [g(t)Ans. f =-g(x), fy=g(y)(g continuous for all t)12) f(x, у, 2) -1+ ху?- 2z'Ans. f=y', f, = 2xy, f, =-4z13) f(x,y,z) = x- \y³ +z°Ans. f, =1, f, =-yly² +z²)"²,-1/2f. =-zly* +z°)²14) f(x,y, z) = sin'(xyz)Ans. f =yz/1–x*y*z²XZfy =/1–x*y*z"хуf =V1–x²y°z²2.2

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Find the Partial Derivatives of the functions with respect to each variable 1 5) f(x,y) = X+y -1 Ans. f- -1 (x+ y}²•I, = - y -1 (xy-1)2" (x+y} -x -1 X+y 6) f(x,y)= ху -1 Ans. fx (ху-1)? 7) f(x,y) = e*»y+1) Ans f = e*y»1), f, = elx-y•1)

Find the Partial Derivatives of the functions with respect to each variable 1 5) f(x,y) = X+y -1 Ans. f- -1 (x+ y}²•I, = - y -1 (xy-1)2" (x+y} -x -1 X+y 6) f(x,y)= ху -1 Ans. fx (ху-1)? 7) f(x,y) = e»y+1) Ans f = ey»1), f, = elx-y•1)

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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Question

Find the Partial Derivatives of the functions with respect to each variable
1
5) f(x,y) =
X+y
-1
Ans. fx-
-1
(x+ y}²• I, =
(x+y}
%3D
%3D
-у' -1
(y-1)2 ]y
Ans f = e*y»1), f, = elx-y•1)
X+y
-x -1
6) f(x,y) =-
ху —1
Ans. fx=
%3D
%3D
(xy-1)²
) f(x,y) = elx*»y«1)
1
1
8) f(x, y) = In(x+y)
Ans. f=
fy
%3D
%3D
X+y
X+y
9) f(x,y)=sin (x-3y)
Ans. f = 2 sin(x- 3y) cos(x- 3y),
fy =-6sin(x- 3y) cos(x- 3y)
10) f(x,y) = x"
Ans f = yx"1, fy, = x' In(x)
11) f(x,y)= [g(t)
Ans. f =-g(x), fy=g(y)
(g continuous for all t)
12) f(x, у, 2) -1+ ху?- 2z'
Ans. f=y', f, = 2xy, f, =-4z
13) f(x,y,z) = x- \y³ +z°
Ans. f, =1, f, =-yly² +z²)"²,
-1/2
f. =-zly* +z°)²
14) f(x,y, z) = sin'(xyz)
Ans. f =
yz
/1–x*y*z²
XZ
fy =
/1–x*y*z"
ху
f =
V1–x²y°z²
2.2

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