Find the derivatives of each of the functions in Exercises 51-62. In some cases it may be convenient to do some prelim- inary algebra. (These exercises involve hyperbolic functions and their inverses.) 51. f(x) = x sinh x3 52. f(x) = x sinh° x 53. f(x) = cosh(In(x² + 1)) 54. f(x) = 3 tanh?e* tanh ĩ 55. f(x) = /cosh² x+1 56. f(x) = Vsinh x 58. f(x) = tanh (tanx²) 57. f(x) = sinh¯'(x³) sinh-1x 59. f(x) = 60. f(x) = x/tanh¬1x cosh- 61. f(x) = sin(esi nh" x) 62. f(x) = cosh-'(cosh¬1 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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Find the derivatives of each of the functions in Exercises
51-62. In some cases it may be convenient to do some prelim-
inary algebra. (These exercises involve hyperbolic functions and
their inverses.)
51. f(x) = x sinh x3
52. f(x) = x sinh° x
53. f(x) = cosh(In(x² + 1))
54. f(x) = 3 tanh?e*
tanh ĩ
55. f(x) = /cosh² x+1
56. f(x) =
Vsinh x
58. f(x) = tanh (tanx²)
57. f(x) = sinh¯'(x³)
sinh-1x
59. f(x) =
60. f(x) = x/tanh¬1x
cosh-
61. f(x) = sin(esi
nh" x)
62. f(x) = cosh-'(cosh¬1 x)
Transcribed Image Text:Find the derivatives of each of the functions in Exercises 51-62. In some cases it may be convenient to do some prelim- inary algebra. (These exercises involve hyperbolic functions and their inverses.) 51. f(x) = x sinh x3 52. f(x) = x sinh° x 53. f(x) = cosh(In(x² + 1)) 54. f(x) = 3 tanh?e* tanh ĩ 55. f(x) = /cosh² x+1 56. f(x) = Vsinh x 58. f(x) = tanh (tanx²) 57. f(x) = sinh¯'(x³) sinh-1x 59. f(x) = 60. f(x) = x/tanh¬1x cosh- 61. f(x) = sin(esi nh" x) 62. f(x) = cosh-'(cosh¬1 x)
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