35, 49, 53,59 with work please. Thank you

216 CHAPTER 3 Differentiation Rules function. If y = xP/4, then y = x. Use implicit different tion to show that 35-38 Find y" by implicit differentiation. 9 y' = 2 x (P/9) - 1 36. x2 + xy + y? = 3 35. x2 + 4y2 = 4 38. x3 - y3 = 7 37. sin y + cos x = 1 49-60 Find the derivative of the function. Simplify where possible. 39. If xy + e" = e, find the value of y" at the point where 49. y = (tan 'x)2 50. y = tan '(x?) * = 0. 40. If x2 + xy + y' = 1, find the value of y" at the point 1 51. y = sin '(2x + 1) 52. g(x) = arccos Vx where x = 1. - 53. F(x) = x sec -'(x3) CAS 41. Fanciful shapes can be created by using the implicit plotting 54. y = tan -'(x - V1 + x2) capabilities of computer algebra systems. 55. h (t) = cot (t) + cot-1(1/t) 56. R(t) = arcsin(1/t) (a) Graph the curve with equation y(yz - 1 ) (y - 2) = x(x - 1)(x - 2) 57. y = x sin 'x + v1 - x2 58. y = cos (sin '1) At how many points does this curve have horizontal b + a cos x tangents? Estimate the x-coordinates of these points. 59. y = arccos OS X- T , a > b > o a + b cos x (b) Find equations of the tangent lines at the points (0, 1) and (0, 2) 1 - x (c) Find the exact x-coordinates of the points in part (a). 60. y = arctan 1 + x (d) Create even more fanciful curves by modifying the equation in part (a). CAS 42. (a) The curve with equation 61-62 Find f'(x). Check that your answer is reasonable by 2y3 + 12 - ys = x4- 2x3+x2 comparing the graphs of f and f'. has been likened to a bouncing wagon. Use a computer 61. f(x) = V1 - x2 arcsin x 62. f(x) = arctan(x] - x) algebra system to graph this curve and discover why. (b) At how many points does this curve have horizontal tangent lines? Find the x-coordinates of these points. 63. Prove the formula for (d/ dx)(cos 'x) by the same method as for (d/ dx) (sin x). 43. Find the points on the lemniscate in Exercise 31 where the tangent is horizontal. 64. (a) One way of defining sec 'x is to say that 44. Show by implicit differentiation that the tangent to the y = sec x sec y = x and 0 sec y = x and O