I would like help with these calculus questions with work, please

Finding a Derivative In Exercises 41-98, find the derivative of the function. 41. g(r) = 5 tan 3.x 42. A(x) = sec .x2 43. y = cos(4 - x) 44. y = sin(x - n) 45. /(x) = exx 46. y = e-x 47. y = evi 48. g(1) = e-3/8 49. y = (sin 2)x3 50. y = cos(xx)2 51. y = 4 sec2 x 52. g(1) = 5 cos' ml 53. f(0) = tan2 50 54. g(0) = cos2 80 55. f(0) = + sin2 20 56. h(t) = 2 cot (mi + 2) 57. f(i) = 3 sec (nt - 1) 58. y = 3x - 5 cos(nx) 59. y = v.x + } sin(2x)2 60. y = sin Vx + /sin.x 61. y = sin(tan 2r) 62. y = cos , sin(tan m.x) 63. h(x) = sin 2r cos 2x 64. g(0) = sec(0/2)tan(0/2) 65. (x) = col .r 66. g(v) = COS V sin x CSC V 67. 8(1) = (e-t + e') 68. y= rex 69. y = In(eth) 70. y = In I ter 2 71. 72. y = 2 73. y = ex - 2xet + 2et 74. y = xet - e 75. ((x) = e- Inx 76. f(x) = e' In.x 77. y = e"(sin x + cos.x) 78. y = In ex 79. g(x) = In .x2 80. A(x) = In(2x2 + 3) 81. y = x- Inx 82. y = (In.x)* 83. y = In(x x - 1) 84. y = In VX - 9 85. f(x) = In 86. f(x) = In 2x x2 + 1 x + 3 87. g() = (In 1)/2 88. h(t) = (In 1)/t 89. y = In x+l 90. y = In 3/ x - 2 X - x+2 91. y = In sin x] 92. y = Injesc x| COs X 93. y = In 94. y = In see x + tan x] COS X - -1 + sin .x 95. y = In 2 + sin .x 96. y = In 1 + sin' x -vr+I 97 + In(x + vx + 1) x+4 98. Y = 212 Im / 2 + + + 4170 Chapter 2 Differentiation Error Analysis In Exercises 99-102, describe and ORoxo Finding an Equation of a Tangent Line In correct the error when finding the derivative of the Exercises 117-124, (a) find an equation of the function. tangent line to the graph of the function at the 99. If y = (1 - x)1/2, then y' = 4(1 - x)-1/2. X given point, (b) use a graphing utility to graph 100. If f(x) = sin? 2x, then f'(x) = 2(sin 2x)(cos 2x). X the function and its tangent line at the point, and (c) use the tangent feature of the graphing 101. utility to confirm your results. 117. f(x) = /7x2 + 9. (4, 1 1) 102. "[re-21] = Me-2x + e-21(4x]) = xle-21(x + 4) X 118. f(x) = (9 - 23)2/3, (1,4) 119. f(x) = sin &x, (7, 0) Slope of a Tangent Line In Exercises 103 and 104, find the slope of the tangent line to the sine function at the 120. y = cos 3x, origin. Compare this value with the number of complete cycles in the interval [0, 2x]. 121. f(x) = tan' x. (#1 ) 103. (a) (b) y = sin 2x 122. y = 2 tan' x. (#2) y = sin x 3.)y = 4 - 12 - In(ex + 1). (0,4) 124. y = 2el-1, (1, 2) Famous Curves In Exercises 125 and 126, find an equation of the tangent line to the graph at the labeled 104. (a) (b) y= sin 3x y'sin point. Then use a graphing utility to graph the function and its tangent line at the point in the same viewing window. 125. Semicircle 126. Bullet-nose curve V/2 -x2 DO Slope of a Tangent Line In Exercises 105-108, find the slope of the tangent line to the graph of the function at the given point. 105. y = ett, (0, 1) 106. y = e-3, (0, 1) 107. y = In x, (1, 0) 108. y = In x3/2. (1, 0) Evaluating a Derivative In Exercises 109-116, find and evaluate the derivative of Horizontal Tangent Line In Exercises 127 and 128, the function at the given point. Use a graphing determine the point(s) at which the graph of the function utility to verify your result. has a horizontal tangent line. 109. y = vx + 8x. (1, 3) 127. f(x) = 2 cos x + sin 2x, 0