Worked problem in calculus. Find the inverse function, check, and verify the derivative rule for the functions (a) f(x) = 3x-2, and (b) g(x) = sqrt(x-3).

1. Definition of ln(x) Using Integration
2. Properties of ln(x) Using Integration
3. End Behavior of ln(x)
4. Derivative of ln(x) as a Slope
5. The Chain Rule for ln(x) and ln|x|
6. Derivative of f(x) = ln(ln(x^2 + 1))
7. Graph of f(x) = 3ln(x-2) + 4
8. Graph of f(x) = ln(x^2 - x)
9. Graph of f(x) = ln|x^2-x|
10. Implicit Differentiation with ln(x)
11. Logarithmic Differentiation
12. Antiderivative of ln(x^4)/x
13. Antiderivative involving 1/x 1
14. Antiderivative involving 1/x 2
15. Trig Antiderivatives involving 1/x
16. Area under f(x) = ln(x)/x
17. Inverse Functions
18. Inverse Functions: ln(x) and exp(x)
19. Graph of f(x) = 2 - e^{2x-1}
20. Inverse Function for f(x) = 2 e^{x-2}
21. No Inverse Function for f(x)=ln(x)-exp(x)
22. Derivative of an Inverse Function
23. Properties of Derivative of exp(x)
24. Derivatives with e^x
25. Tangent Line to x^2 e^x at x=1
26. Graph of f(x) = x^2 e^{-x}
27. Graph of Normal Distribution
28. Implicit Differentiation with e^x
29. Indefinite Integrals with e^x
30. Definite Integral of exp(-3x+2) (HD Version)
31. Definite Integral of (e^x - 1)(e^x - 2)/e^2x (HD Version)
32. Graphing with 2^x
33. Equations with Logarithms
34. Derivatives of log_b(x) and b^x
35. Tangent Lines to log_b(x) and b^x
36. Logarithmic Differentiation
37. Indefinite Integrals with b^x and log_b(x)
38. Definite Integrals with b^x and log_b(x)
39. Compound Interest
40. Evaluating Inverse Trig Functions 1
41. Evaluating Inverse Trig Expressions 2
42. Evaluating Inverse Trig Expressions 3
43. Derivatives of Inverse Trig Functions
44. Graph of f(x) = tan^{-1}(1-x^2)
45. Tangent Line to f(x) = xsin^{-1}(x/2)
46. Integrals with Inverse Trig Functions 1
47. Integrals with Inverse Trig Functions 2
48. Integrals with Inverse Trig Functions 3

In this third installment, Dr. Bob resumes his Calculus series by solving derivatives and definite integrals of special functions: Derivative of ln(x), Integration with ln(x), Inverse functions, Derivative and integral with e^x, Other Bases, Derivatives of Inverse Trig, Integrals of Inverse Trig.