Chapter 5 AP Calculus AB Differentiation by Logarithmic, Exponential, and Transcendental Functions

1. Chapter 5 AP Calculus ABDifferentiation by Logarithmic, Exponential, and Transcendental Functions

2. Theorem 5.1 • Properties of the Natural Logarithmic Function • The domain is (0,∞) and the range is (-∞,∞) • The function is continuous, increasing, and one to one • The graph is concave downward

3. Theorem 5.2 • Logarithmic Properties • Ln(1)=0 • Ln(ab)=lna+lnb • Ln(a^n)=nln(a) • Ln(a/b)=ln(a)-ln(b) • Definition of e

4. Theorem 5.3+5.4+5.5

5. Theorem 5.6: Reflective Property • The graph of g contains the point (a,b) if and only if f^-1 contains point (b,a) • Inverse Function Definition: • f(g(x))=x for each x in the domain of g • g(f(x))=x for each x in the domain of f

6. Theorem 5.7 • A function has an inverse function if and only if it is one to one • If f is strictly monotonic on its entire domain, then it is on to one and therefore has an inverse function

7. Theorem 5.8

8. Theorem 5.9: Derivative of an Inverse Function

9. Properties of the Natural Exponential Function

10. Theorem 5.11+5.12

11. Theorem 5.13

12. Theorem 5.14