Find all the second order partial derivatives of the given function. f(x, y) = In (x 2y - x) O a2€ _ 2xy - 2x2y² - 1. a²£ dx2 x2 x2 %3D = - %3D = - dydx дхду (x?v - x}² a2t _ 2xy - 2x2y2 -1. (x?y - x)² dy2 (x?y -x) (x²y - x)? x2 = - %3D = - dx2 dy? (x2y - x)² ' dyəx dxdy (x²y - x)² azf xy - x2y2 - 1 a2f dx2 (x2y - x)² 'dy2 a2f dxdy x2 = - = - (x2y - x)2' dydx (x?y - x)? a2t _ 2xy - 2x2y2 -1. (x?y - x}² x2 (x?y - x}² = = dx2 dy (x2y - x)²' dyəx əxdy
Find all the second order partial derivatives of the given function. f(x, y) = In (x 2y - x) O a2€ _ 2xy - 2x2y² - 1. a²£ dx2 x2 x2 %3D = - %3D = - dydx дхду (x?v - x}² a2t _ 2xy - 2x2y2 -1. (x?y - x)² dy2 (x?y -x) (x²y - x)? x2 = - %3D = - dx2 dy? (x2y - x)² ' dyəx dxdy (x²y - x)² azf xy - x2y2 - 1 a2f dx2 (x2y - x)² 'dy2 a2f dxdy x2 = - = - (x2y - x)2' dydx (x?y - x)? a2t _ 2xy - 2x2y2 -1. (x?y - x}² x2 (x?y - x}² = = dx2 dy (x2y - x)²' dyəx əxdy
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...
Related questions
Question
Transcribed Image Text:Find all the second order partial derivatives of the given function.
f(x, y) = In (x 2y - x)
O a2t _
2xy - 2x2y2-1 a2f
x2
a2f
x2
= -
= -
dx2
(x²y - x)²
dy?
(x²y - x)²' dydx¯ dxdy
(x²y - x)²
2xy - 2x2y2 - 1, aZ£
(x²y - x}² 'ay?
az£ _ xy - x²y2 - 1 22f
dx2
x4
a2f
a2f
x2
(x2y - x)²
dydx
dxdy
(x²y - x}²
x4
x2
= -
(x²y - x}² 'ay2
O a2f
(x²y - x)² ' dyðx
дхду
(x²y - x}²
2xy - 2xy2 - 1, a2¢
(x2y - x)²
x4
x2
%D
dy? (x2y - x)
avdx
дхду
(x?y - x)²
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning