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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Please help with just D, please
![a. If f(x, y) = 3x³ - 2x2y5, find the partial derivatives fz and fy.
+₁=2
Əx
-(2x³ - 2x²y4) = 9x² - 4x4
fy=2(3x³-2x2y4) = -8x2y3
find the partial derivatives fr and fy.
b. If f(x, y) =
ry²
x+1'
fx
Fx = 2 (x4² ) = (x+1) y ² - xy² = 24/1/2 = (x + 1/²
2
=42
(x+1)2
(X+1) (x+1²
xy=-3 (2-) = 2x4
c. If g(r, s) = rs cos(r), find the partial derivatives g, and g..
g(₁,5) = rscos(r)
g₁= = (cos(r)) = S(os(c)-rssin (r)
dr.
gs=d& (rescos (r)) = rcsos (r)
d. Assuming f(w, x, y) = (6w+1) cos(3x² + 4xy³ + y), find the partial
derivatives fw, fa, and fy.
x2z³
1+1²
e. Find all possible first-order partial derivatives of g(x, t, z) =
9-=-2 (x² + 3³²) = x² + 2²-1-(23)
x2+z3
2+
9x=2+₂ ³
1+23
2
+ 2₂2 = 3x² ¹/2 ²
1+23
-3_x³² 2 5
[1+2³]²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F600ed388-36fd-4fb9-9b36-752c39730667%2Fd3dd471b-f53e-4c50-85e7-e48e9475a56c%2Fbh2s9r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a. If f(x, y) = 3x³ - 2x2y5, find the partial derivatives fz and fy.
+₁=2
Əx
-(2x³ - 2x²y4) = 9x² - 4x4
fy=2(3x³-2x2y4) = -8x2y3
find the partial derivatives fr and fy.
b. If f(x, y) =
ry²
x+1'
fx
Fx = 2 (x4² ) = (x+1) y ² - xy² = 24/1/2 = (x + 1/²
2
=42
(x+1)2
(X+1) (x+1²
xy=-3 (2-) = 2x4
c. If g(r, s) = rs cos(r), find the partial derivatives g, and g..
g(₁,5) = rscos(r)
g₁= = (cos(r)) = S(os(c)-rssin (r)
dr.
gs=d& (rescos (r)) = rcsos (r)
d. Assuming f(w, x, y) = (6w+1) cos(3x² + 4xy³ + y), find the partial
derivatives fw, fa, and fy.
x2z³
1+1²
e. Find all possible first-order partial derivatives of g(x, t, z) =
9-=-2 (x² + 3³²) = x² + 2²-1-(23)
x2+z3
2+
9x=2+₂ ³
1+23
2
+ 2₂2 = 3x² ¹/2 ²
1+23
-3_x³² 2 5
[1+2³]²
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