21. v = 22. y 1 - er 59. 23. y = V1 + 2835 24. y = e" cos 4t 61. Find y 25. y - 5-1/x 26. y = 10!- 62. Find 27. F(1) = e'sin 2 xe ' + 28. y = - 63. Find 29. y = In |2 - x - 5x? | 30. y = VI + xe 64. Find 31. f (1 ) = tan(e ' ) + ent 32. y = 65. The 33. y = In(e"* + xe ' ) 34. y = [In(1 + ex)]2 a dan mod 35. y = 2x log10 Vx 36. y = x2e-1/x sine 37. f (1) = sin? (e sing) poin 38. y = logz(e * cos Tx) 39. g(x) = (2ra" + n)" 40. y = 23+2 when the 41-44 " Find y' and y". velo 41. y = e"* sin Bx 42. y = _ 66. Und the 43. y = xin r 44. y = In(sec x + 45-46 - Find an equation of the tangent line to the curve at the who given point. the 45. y = In(x2 - 3x + 1). (3.0) 46. y = e/x. (1. e) (a) ( b ) (c) 47-48 . Differentiate f and find the domain of f. 47. f(x ) =7 - 1 - In - In(x - 1) 48. f (x) = In In In x 67. Sho dif 49. Let f(x) = ex + In(cos x). For what value of c is 68. For F'(T/4) =67 equ 50. Let f(x) - loga(3x2 - 2). For what value of a is f'(1) = 3? 69. IfJ 70. Fin 51-60 - Use logarithmic differentiation or an alternativeFIGURE 4 aF 2 + In x 2Vx (as in Solution 3.3 EXERCISES 1-40 - Differentiate the function. 11. g(x) = In(x vx2 - 1) 12. h(x) = In(x + Vx2 - 1) 1. f(x) - logo(x 2. f (x) = x In x 3. f(x) = sin(In x) 4. f(x) = In(sin x) 13. G(y) = In - (2y + 1)5 Vy2 + 1 14. g(r) = r2 In(2r + 1) 5. f (x) = In - 6. y 15. F(s) = In In s 16. y - In cos(In x) In x 7. f(x) = sin x In(5x) 8. f(x) = logs(xe') 17. y = tan [In(ax + b)] a- - z2 18. H(z) = In\\ Vaz+ z2 9. g(x) = In - 10. f(u) 1 + In u 19. f ( x) = (x' + 2x)er 20. g(x) = Vx ex Unless otherwise noted, all content on this page is @ Cengage Learning. rave NFIGURE 4 aF 2 + In x 2Vx (as in Solution 3.3 EXERCISES 1-40 - Differentiate the function. 11. g(x) = In(x vx2 - 1) 12. h(x) = In(x + Vx2 - 1) 1. f(x) - logo(x 2. f (x) = x In x 3. f(x) = sin(In x) 4. f(x) = In(sin x) 13. G(y) = In - (2y + 1)5 Vy2 + 1 14. g(r) = r2 In(2r + 1) 5. f (x) = In - 6. y 15. F(s) = In In s 16. y - In cos(In x) In x 7. f(x) = sin x In(5x) 8. f(x) = logs(xe') 17. y = tan [In(ax + b)] a- - z2 18. H(z) = In\\ Vaz+ z2 9. g(x) = In - 10. f(u) 1 + In u 19. f ( x) = (x' + 2x)er 20. g(x) = Vx ex Unless otherwise noted, all content on this page is @ Cengage Learning. rave N39. 960 where's i the veloci 41-44 - Find y and v velocity 41. v = e" sin Bx In x 66. Under ce the equa 43. y = x In x 44. y = In(sec x + tan x) 45-46 . Find an equation of the tangent line to the curve at the where p given point the rum 45. y = In(x' - 3x + 1). (3.0) 46. y = e'/x. (1, e) (a) Find (b) Find (c) Grap 47-48 " Differentiate f and find the domain of f. in ho for 8 47. f ( x) = ]- In(x - 1) 48. f(x) = In In In x 67. Show th different 49. Let f(x) = cx + In(cos x). For what value of c is 68. For what f'(TT/4) =6? equation 50. Let f(x) = loga(3x2 - 2). For what value of a is f'(1) = 3? 69. If f (x) 70. Find the 51-60 . Use logarithmic differentiation or an alternative method to find the derivative of the function. 71. Find a fo 51. y = (x2 + 2)? (x4 + 4)# e 'cosx 52. * = 2 + x + 1 72. Find- 53. M - VH F 1 54. y = Vxe" "(x + 1)20 73. If f(x) 55. y = x 56. y - XO. 74. Evaluate 57. y = (cos x)" 58. V = VT59. v = (tan ,) 60. v = (sin x) x 61. Find v' if e = x + y. 62. Find an equation of the tangent line to the curve xe + ye' = 1 at the point (0, 1). 63. Find y' if y = In(x2 + y?). 64. Find y' if x' = y'. 65. The motion of a spring that is subject to a frictional force or a damping force (such as a shock absorber in a car) is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion of a point on such a spring is s(1) = 2e s' sin 2 uf where s is measured in centimeters and / in seconds. Find the velocity after / seconds and graph both the position and velocity functions for 0 = / = 2. 66. Under certain circumstances a rumor spreads according to the equation p(1) 1 + ae where p(f) is the proportion of the population that knows onstants