Find all the second order partial derivatives of the given function. f(x, y) = cos (xy²) = -y4 cos xy²; 24 di = 2x[2xy² cos (xy2) + sin(xy²)]; - 2² - 2y[xy² cos (xy²) + sin(xy²)]; = y² sin xy²; 3= 2[2y² cos (xy²) - sin (xy³] ; ; 2f 22 ayax Zi ayax = - y² sin xy²; 1 = 2[ sin (xy²)- 2y² cos (xy²)]; - Zt dyax = - y² sin xy²; 2 = 2y[2y² cos (xy-²) – sân (x3 कर के Fi (xy²)]; əvəx ZE axay Zi axoy Zi axay = 2y[y2 cos (xy2) - sin (xy²)] = = 2y [sin (xy2)-y² cos (xy²)] Zi axoy = 2[v² cos(xy²)- sin(xy²)]
Find all the second order partial derivatives of the given function. f(x, y) = cos (xy²) = -y4 cos xy²; 24 di = 2x[2xy² cos (xy2) + sin(xy²)]; - 2² - 2y[xy² cos (xy²) + sin(xy²)]; = y² sin xy²; 3= 2[2y² cos (xy²) - sin (xy³] ; ; 2f 22 ayax Zi ayax = - y² sin xy²; 1 = 2[ sin (xy²)- 2y² cos (xy²)]; - Zt dyax = - y² sin xy²; 2 = 2y[2y² cos (xy-²) – sân (x3 कर के Fi (xy²)]; əvəx ZE axay Zi axoy Zi axay = 2y[y2 cos (xy2) - sin (xy²)] = = 2y [sin (xy2)-y² cos (xy²)] Zi axoy = 2[v² cos(xy²)- sin(xy²)]
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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![Find all the second order partial derivatives of the given function.
f(x, y) = cos (xy²)
2
= -y4 cos xy²;
d
di
2²
- 2y[xy² cos (xy²) + sin(xy²)];
- - y² sin xy²,
=
2x[2xy² cos (xy2) + sin(xy²)]; -
= y² sin xy²; 2 = 2[2y² cos (xy²) - sin (xy³)] ; ;
Zi
a
əyax
1
= 2[ sin (xy²)- 2y² cos (xy²)]; -
Fi ZE
ἀὸν
ay ax
Ft
ay ax
=
21 = - y² sin xy², 1 = 2y [2y² cos (
= 2y[2y² cos (xy²) – sin (xy²)] ; -
Fi
के
Zi
axay
Zi
axay
= 2y[y2 cos (xy2) - sin (xy²)]
Zi
độ đội
2y [sin (xy2)-y² cos (xy²)]
= 2[v² cos(xy²) - sin(xy-²)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62e8d7fc-408a-4994-8f93-a3f5b4fef9f8%2F2d0ffa15-8d5c-4f72-9176-73f3bc435ab8%2Fh5cxel_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find all the second order partial derivatives of the given function.
f(x, y) = cos (xy²)
2
= -y4 cos xy²;
d
di
2²
- 2y[xy² cos (xy²) + sin(xy²)];
- - y² sin xy²,
=
2x[2xy² cos (xy2) + sin(xy²)]; -
= y² sin xy²; 2 = 2[2y² cos (xy²) - sin (xy³)] ; ;
Zi
a
əyax
1
= 2[ sin (xy²)- 2y² cos (xy²)]; -
Fi ZE
ἀὸν
ay ax
Ft
ay ax
=
21 = - y² sin xy², 1 = 2y [2y² cos (
= 2y[2y² cos (xy²) – sin (xy²)] ; -
Fi
के
Zi
axay
Zi
axay
= 2y[y2 cos (xy2) - sin (xy²)]
Zi
độ đội
2y [sin (xy2)-y² cos (xy²)]
= 2[v² cos(xy²) - sin(xy-²)]
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