Find the Partial Derivatives of t 1) f(x,y) = 2x - 3y -4 2) S(x, y) = (x' -1Xy+ 2) 3) f(x, y) = (xy-1}

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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11:-1
37 - 51.pdf >
Exercises
Find the Partial Derivatives of the functions with respect to each variable
1) f(x,y) = 2x - 3y-4
Ans. f, 4x, f, =-3
2) f(x, y) = (x* -1)Xy+ 2)
Ans. f,= 2x(y+ 2), f, = x' -1
3) f(x, y) = (xy-1)
Ans. f, = 2y(xy-1), f, 2x(xy-1)
4) S(x, y) = Vx² + y°
Ans. f,=T+ys Ja +y*
42
Mathematics
Second Year
Electrical & Electronic Engineering Department
Dr. Atheer Alaa Sabri
-1
f%3D
(x+y)
-1
f(x, y) =
x+y
5)
Ans. f, =
(r+ y}
-x' -1
- y' -1
(ху— 1)?
x+y
6) f(x, y)=-
xy -1
Ans. f. =
(xy-1)
7)
f(x, y) = e*y+1)
Ans. f. =e*y+1), f. = e*+y+1)
1
f,
x+ y
1
8)
f(x, y) = In(x+ y)
Ans. f, =
x+y
9) S(x, y) = sin'(x-3y)
Ans. f, =2 sin(x-3y)cos(x-3y),
f, =-6 sin(x-3y) cos(x-3y)
10) f(x, y) =x'
Ans. f, = yx, f, = x' In(x)
11) f(x.y) =Jg()dt,
Ans. f, =-g(x), f, = g(y)
(g continuous for all t)
12) f(x, y,z) = 1+xy- 22
Ans. f,=y', f, = 2.xy, f, =-4z
13) f(x, y,z) =x-Vy? +z
Ans. f, =1, f, =-yly* +z')"²,
S. =--(y* +=')"?
%3D
II
Transcribed Image Text:11:-1 37 - 51.pdf > Exercises Find the Partial Derivatives of the functions with respect to each variable 1) f(x,y) = 2x - 3y-4 Ans. f, 4x, f, =-3 2) f(x, y) = (x* -1)Xy+ 2) Ans. f,= 2x(y+ 2), f, = x' -1 3) f(x, y) = (xy-1) Ans. f, = 2y(xy-1), f, 2x(xy-1) 4) S(x, y) = Vx² + y° Ans. f,=T+ys Ja +y* 42 Mathematics Second Year Electrical & Electronic Engineering Department Dr. Atheer Alaa Sabri -1 f%3D (x+y) -1 f(x, y) = x+y 5) Ans. f, = (r+ y} -x' -1 - y' -1 (ху— 1)? x+y 6) f(x, y)=- xy -1 Ans. f. = (xy-1) 7) f(x, y) = e*y+1) Ans. f. =e*y+1), f. = e*+y+1) 1 f, x+ y 1 8) f(x, y) = In(x+ y) Ans. f, = x+y 9) S(x, y) = sin'(x-3y) Ans. f, =2 sin(x-3y)cos(x-3y), f, =-6 sin(x-3y) cos(x-3y) 10) f(x, y) =x' Ans. f, = yx, f, = x' In(x) 11) f(x.y) =Jg()dt, Ans. f, =-g(x), f, = g(y) (g continuous for all t) 12) f(x, y,z) = 1+xy- 22 Ans. f,=y', f, = 2.xy, f, =-4z 13) f(x, y,z) =x-Vy? +z Ans. f, =1, f, =-yly* +z')"², S. =--(y* +=')"? %3D II
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