Please answer the following questions #8, 10, 54, 56, 58, 64, 68

It would be really helpful if you can use the chain rule or product if it can be applied to the exercises.

Do exercises, following the same exact format from the examples that are going to be provided.

52. g(x) = In tan x 53. f(x) = In (In 4x) 54. f(x) = In (In 3x) - 55. S(x) = In X 56. f(x) = In + 5 57. S(x) = ex In x X 58. f(x) = e2x In x 59. S(x) = ex sec x 60. f(x) = (sin 2x)e* 61. S(x) = In (ex + 1) 62. f(x) = In (ex - 2) 63. S(x) = (In x)2 64. f(x) = (In x)3 65. y = (In x) -4 66. y = (In x)" 67. f(t) = In (13 + 1)5 68. J(t) = In (12 + 1) 3 69. S(x) = [In (x + 5)]4K. CC A population grows exponentially at an average growth 37. y = rate of r percent each year and an initial population of No. Compute the population at times t = 1, t = 2, and 39. y = t = 5 given 41. y 7. No = 1000, r = 20%. 8. No = 50, r = 5%. 42. y = 9. No = 286,000,000, r = 2.1%. 43. y = 10. No = 50,000,000, r = 1.9%. 45. y =calculator Solve for T write In (0 . 00 ) /- 0.02 35) et = 100 41 1 ) e-0. 021 = 0.06 Loge 100 = T Base - e In 10o = T exponent = - 0. 027 T = 4. 605170 Loge 0.06 =+ 0.0271 - 8. 02 - 0/027 Differentiate T= In0. 06 43 ) y = - 6 Inx 1 - 0.02 T= 140. 670536 d Inx = 1 j d Inf (x ) = f ( x ) dx dx F( y ) cly = - 6 ( # ) = 6 dx X oct 45 ) 1 = * " Inx -1 * 2 2 - > f = X 4 ( ) = 41 X 3 --simplify " = (# ) do = (x 3 ( inx + x " ( * ) - X 1 ( 2 X) = - X 4 x 3 / n x + * 3 _ x 2