Homework Help is Here – Start Your Trial Now!
Math
Calculus
əz дz Find and ax if z is defined implicitly as a function of x and y by the equation ay + +z6+ 18xyz - 30 = 0. Then evaluate these partial derivatives at the point (-1, 1, 2). Solution дz To find we differentiate implicitly with respect to x, being careful to treat y as a instant and z as a function (of > ах' 6x5 əz +625 əx +18yz + 18xy. дz Əx = 0 5+3yz əz Solving this equation for we obtain ах' дz ax 3xy + z³ дz 3xz+y Similarly, implicitly differentiation with respect to y gives. ду 3xy+z5 Notice that the point (-1, 1, 2) satisfies the equation x6+y+z6+ 18xyz - 30 = 0 so it lies on the surface. At this point дz ax дz ду

əz дz Find and ax if z is defined implicitly as a function of x and y by the equation ay + +z6+ 18xyz - 30 = 0. Then evaluate these partial derivatives at the point (-1, 1, 2). Solution дz To find we differentiate implicitly with respect to x, being careful to treat y as a instant and z as a function (of > ах' 6x5 əz +625 əx +18yz + 18xy. дz Əx = 0 5+3yz əz Solving this equation for we obtain ах' дz ax 3xy + z³ дz 3xz+y Similarly, implicitly differentiation with respect to y gives. ду 3xy+z5 Notice that the point (-1, 1, 2) satisfies the equation x6+y+z6+ 18xyz - 30 = 0 so it lies on the surface. At this point дz ax дz ду

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
дz дz Find and if z is defined implicitly as a function of x and y by the equation Əx ду x6 + y +z6+ 18xyz - 30 = 0. Then evaluate these partial derivatives at the point (-1, 1, 2). Solution дz To find we differentiate implicitly with respect to x, being careful to treat y as a instant and z as a function (of > " Əx дz 6x +625 дz Əx +18yz + 18xy. = 0 Əx дz Solving this equation for we obtain Əx Əx 3xy + z дz Similarly, implicitly differentiation with respect to y gives 3xz+y5 25 Əy 3xy + z Notice that the point (-1, 1, 2) satisfies the equation x6 + y + z6 + 18xyz - 30 = 0 so it lies on the surface. At this point дz Əx дz ду = 11 +3yz
Transcribed Image Text:дz дz Find and if z is defined implicitly as a function of x and y by the equation Əx ду x6 + y +z6+ 18xyz - 30 = 0. Then evaluate these partial derivatives at the point (-1, 1, 2). Solution дz To find we differentiate implicitly with respect to x, being careful to treat y as a instant and z as a function (of > " Əx дz 6x +625 дz Əx +18yz + 18xy. = 0 Əx дz Solving this equation for we obtain Əx Əx 3xy + z дz Similarly, implicitly differentiation with respect to y gives 3xz+y5 25 Əy 3xy + z Notice that the point (-1, 1, 2) satisfies the equation x6 + y + z6 + 18xyz - 30 = 0 so it lies on the surface. At this point дz Əx дz ду = 11 +3yz
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS