Find the derivative of the following: 1. y = 3-2x 3+2x 2. y (x²+4)²(2x³ — 1)³ = 3. If y = x² - 4x and x = √2t² + 1, find y'when t = √2 4. Find dy given x = dx' 5.y = x2 √4-x² 6. Find y" if x³ - 3xy + y² = 1 A 7. Find dy dx' dy dx 8. Find x² + 2x =y√1-y² given y = u³ + 4, u = x √√x-1 10. Find y", given x² - xy + y² = 3 9. Find y", given y a. y' = 42(5-2√5) dy dx = b. c. y" e. y' f. y" d. dy = 6x²(x + 2)²(x + 1) dx h. 5 4(x-1)2 given y = √1+u, u = √x gy' = 2x(x² + 4)(2x³ − 1)² (13x³ + 36x − 2) dy dx i. y" j. = dy = dx = = = 8x-x3 (4-x²)2 -4xy (y²-x)3 = = -12 (3+2x)² 4-x √1-y² 1-2y² 18 (x-2y)² 1 4√x+x√x
Find the derivative of the following: 1. y = 3-2x 3+2x 2. y (x²+4)²(2x³ — 1)³ = 3. If y = x² - 4x and x = √2t² + 1, find y'when t = √2 4. Find dy given x = dx' 5.y = x2 √4-x² 6. Find y" if x³ - 3xy + y² = 1 A 7. Find dy dx' dy dx 8. Find x² + 2x =y√1-y² given y = u³ + 4, u = x √√x-1 10. Find y", given x² - xy + y² = 3 9. Find y", given y a. y' = 42(5-2√5) dy dx = b. c. y" e. y' f. y" d. dy = 6x²(x + 2)²(x + 1) dx h. 5 4(x-1)2 given y = √1+u, u = √x gy' = 2x(x² + 4)(2x³ − 1)² (13x³ + 36x − 2) dy dx i. y" j. = dy = dx = = = 8x-x3 (4-x²)2 -4xy (y²-x)3 = = -12 (3+2x)² 4-x √1-y² 1-2y² 18 (x-2y)² 1 4√x+x√x
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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Transcribed Image Text:Find the derivative of the following:
1. y =
=
5. y
3-2x
3+2x
2. y = (x²+4)²(2x³ — 1)³
-
3. If y = x² - 4x and x = √√2t² + 1,
√2
find y'when t = V
dy
4. Find
given x = y√1-y²
=
7. Find
A
-x
6. Find y" if x³ - 3xy + y³ = 1
dy
dx
dy
given y
=
8. Find
x² + 2x
9. Find y", given y =
given y
=
u³ +4, u =
x
x-1
10. Find y", given x² - xy + y² = 3
4√2
a. y' = ¹/2 (5-2√5)
5
b.
c. y"
dy
dx
-12
(3+2x)²
4-x
5
4(x-1)2
√1+u, u = √√x gy' = 2x(x² + 4) (2x³ − 1)² (13x³ + 36x - 2)
e. y'
dy
d. = 6x²(x + 2)²(x + 1)
dx
f. y"
h.
j.
dy
dx
i. y"
=
dy
dx
=
=
8x-x3
(4-x²)2
-4xy
(y²-x)³
=
=
B
√1-y²
1-2y2
18
(x-2y)²
1
4√x+x√x
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