Question 6 and 29

3.6 Exercises 1. Explain why the natural logarithmic function y = In x is used much more frequently in calculus than the other logarithmic functions y = log x. 2-26 Differentiate the function. 2. g(1) = In(3 + 3) 3. /(x) = In(x + 3x + 5) 4. [(x) = x Inx - x 5. f(x) = sin( In x) 6. f(x) = In(sin*x) 7. f(x) = In - 8. V= X In x 9. g(x) = In(xe -2) 10. g(t) = v1 + In 11. Fir) = (In ) sin 12. p() = Inv/13 + 1 13. y = log,(x] + 3x) 14. y = log10 sec x In v 15. F(s) = In In s 16. P(p) = 1 - 17. T(@) = 2' log12 18. g(7) - In 3 21 - 1 19. y = In 3 - 2x*| 20. y = In(csc x - cot x) 21. y = In(e * + xe"' ) 22. g(x) = exlax 23. h(x) = er +inx 1 + 2x 24. y = \\ 1 - 2x 25. y = In 26. y = log: (x logs x) 27. Show that -In(x + vx' + 1 = ar VX- + 1 d 1 - COS X 28. Show that - In = CSC X. dx 1 + cos x 29-32 Find y' and y". In x 29. y = vx In x 30. V = 1 + In .x 31. y = In sec x 32. y = In(1 + In x) 33-36 Differentiate f and find the domain of f. 33. ((x) = 1 - In(x - 1) 34. /(x) = v2 + Inx