Questions: 3, 7, 13, 19, 23, 27, 31, 37,43,49,51Please show work. Thank you

SECTION 3.6 Derivatives of Logarithmic Functions 223 rithmuc 3.6 EXERCISES 1. Explain why the natural logarithmic function y - In x is used 33-34 Find an equation of the tangent line to the curve at the much more frequently in calculus than the other logarithmic given point. functions y = log,x (33. y = In(x - 3 + 1). (3, 0] 2-22 Differentiate the function. 34. y = x Inx. (1. 0) 2 f(x] - xiox - x 3. f(x) = sin(In x) 4. fix) - In(sin'x) 2 35. If f(x) - sin x + In x, find f'(x). Check that your answer is reasonable by comparing the graphs of f and f_ (5. fix) - In = 6. y= In x 4:36. Find equations of the tangent lines to the curve y - (In x)/r at the points (1. 0) and (e. I/e). Illustrate by graphing the 7. fix) = logiall + cos x) 8. f(r) = logive curve and its tangent lines. 9. (x) = InGre an) 10. (f) - VI+ Inr 37. Let f(x) = cx + In(cos x). For what value of c is (7/4) - 67 11. F() = (In t) sin r 12 h(x) = In(x + vx - 1) 38. Let f(x) - log,(3x] - 2). For what value of b is f'(1) = 3? 13. G( y) - In- (2y + 1) In t 14. P(D) = 39-50 Use logarithmic differentiation to find the derivative of the 1 - 0 function. 39. y = (r) + 2) (x' + 4)" cos x 15. F(s) - In In's 16. y = In | 1 + 1-") 40. -17, T() = 2' log:2 18. y = In(csc x - col x) 41. y X - 1 42. y - Vie" (r + 1) 20. H(z) = In \\+z (43. y= x 44. = 45. = x 46. y = (VI) 21. y = tan[ Infax + b)] 22. y = log, (x logs x) 47. y = (cos .x)" 48. y - (sin.() 23-26 Find y' and y 49. y - (tan x) )/ 50. y - (In x) 23. y = vr Inx 24. y = = In x I + In x 51. Find y' if y - In(x] + y? ) 25. y = In | sec x 26. y - In() + In x) 52. Find y if x y' 27-30 Differentiate f and find the domain of 53. Find a formula for fe(x) if f(x) - In(x - 1). 27. (x) - 1 - In(x - 1) 28. f (x) - 2+ Inx 54. Find 29. f(x) = Intri - 2x) 30. f(x) - In In In x 55, Use the definition of derivative to prove that lim In(1 + 2) - 1 31. If /(x) = In(x + In x). find S'(1). 32. If f(x) = cos( In x ). find f(1). 56. Show that lim (1 + 4 - e' for any x > 0