Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 41E
Related questions
Question
![02
Chapter 3: Differentiation
43. y = sin (cos (2t - 5))
44. y = cos (5 sin
cises
45. y =
(1 + cos" (71))"
1+ tan
46. y =
47. y = VI + cos (1)
48. y = 4 sin (V1 + Vi)
Second Derivatives
Find y" in Exercises 49-52.
(1+ )
cot (3x - 1)
49. у
zises
(1 - Vi)
50. у
()
51. y =
52. y = 9 tan
Finding Numerical Values of Derivatives
In Exercises 53-58, find the value of (f g)' at the given value of x.
53. f(u) u + 1, u g(x) = Vx, x 1
zises 54. f(u) = 1 -
u = g(x) =
x = -1
%3D
1-.
55. f(u) = cot
u = g(x) = 5Vĩ, x= 1
10
56. f(и)- и +
u = g(x) = Tx, x = 1/4
cos u
2u
57. f(u) =
u = g(x) = 10r² + x + 1, x= 0
u? + 1
58. f(u) =
u = g(x) = - 1, x= -1
%3D
u+
59. Suppose that functions f and g and their derivatives with respect
to x have the following values at x 2 and x = 3.
f(x)
g (x)
f'(x)
g'(x)
8.
1/3
-3
-4
5
Find the derivatives with respect to x of the following combina-
tions at the given value of x.
а. 2/(х), х 2
b. f(x) + g(x), x= 3
c. f(x) g(x), x= 3
d. f(x)/g(x), x= 2
e. f(g(x)), x = 2
f. Vf(x). x = 2
g. 1/g (x), x 3
h. Vf(x) + g*(x), x = 2
60. Suppose that the functions f and g and their derivatives with re-
spect to x have the following values at x 0 and x = 1.
f(x)
g(x)
f'(x)
g'(x)
1
5
1/3
-8/3
3
-4
-1/3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b3f7929-21d9-46b8-8dd1-9852cd832fb9%2F25fde86a-7886-40cd-8b86-2bf51d95203e%2F44rg1q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:02
Chapter 3: Differentiation
43. y = sin (cos (2t - 5))
44. y = cos (5 sin
cises
45. y =
(1 + cos" (71))"
1+ tan
46. y =
47. y = VI + cos (1)
48. y = 4 sin (V1 + Vi)
Second Derivatives
Find y" in Exercises 49-52.
(1+ )
cot (3x - 1)
49. у
zises
(1 - Vi)
50. у
()
51. y =
52. y = 9 tan
Finding Numerical Values of Derivatives
In Exercises 53-58, find the value of (f g)' at the given value of x.
53. f(u) u + 1, u g(x) = Vx, x 1
zises 54. f(u) = 1 -
u = g(x) =
x = -1
%3D
1-.
55. f(u) = cot
u = g(x) = 5Vĩ, x= 1
10
56. f(и)- и +
u = g(x) = Tx, x = 1/4
cos u
2u
57. f(u) =
u = g(x) = 10r² + x + 1, x= 0
u? + 1
58. f(u) =
u = g(x) = - 1, x= -1
%3D
u+
59. Suppose that functions f and g and their derivatives with respect
to x have the following values at x 2 and x = 3.
f(x)
g (x)
f'(x)
g'(x)
8.
1/3
-3
-4
5
Find the derivatives with respect to x of the following combina-
tions at the given value of x.
а. 2/(х), х 2
b. f(x) + g(x), x= 3
c. f(x) g(x), x= 3
d. f(x)/g(x), x= 2
e. f(g(x)), x = 2
f. Vf(x). x = 2
g. 1/g (x), x 3
h. Vf(x) + g*(x), x = 2
60. Suppose that the functions f and g and their derivatives with re-
spect to x have the following values at x 0 and x = 1.
f(x)
g(x)
f'(x)
g'(x)
1
5
1/3
-8/3
3
-4
-1/3
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