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
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
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
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