| Find the derivatives of each of the functions in Exercises In some cases it may be convenient to do some pre- liminary algebra. In(3x²) 34. f(x) = 3x² Inx 33. f(x) = tan x tanx 35. f(x) = sin(Inx) 36. f(x) = In(x sin x) 37. f(x) = sin-'(3x²) 38. f(x) = 3(sin¬1x)² 39. f(x) = x² arctan x2 40. f(x) = tan-'(lnx) 41. f(x) = sec-1x² 42. f(x) = sin(sin¬1 x) 43. f(x) = sin='(sec² x) 44. f(x) = sin (sec-1x) sin-1x tan=1x sin-1x 45. f(x) = 46. f(x) = sec-1x 47. f(x)=In(arcsec (sin²x)) 48. f(x) — х-2 еtx sin-1x sin(arcsin x) 49. f(x) = sec(1+tan¬1 x) 50. f(x) = arctan x

Evaluate f' () and f" () if f(x) = (sin|x|)|tanx|

Find the derivative f(x) for each function given below a) f(x) = (1+ex) (1-ex) b) f(x) = x² inx ) f cx) = 5x3 (Cosx - sinx) 4

Textbook Videos [+] Consider the function f(x) whose second derivative is f''(x) = 9x + 8 sin(x). If f(0) = 2 and f'(0) =-2, what is f(5)?