1. Derivatives and Integrals of Natural Logarithms
5-B

2. Natural Logarithms
Natural logarithm is the logarithm with base e , where e≈
1) Find

3. Properties of Logarithmsb) c) d) e)

4. Graph of y = ln x Domain (0,∞) and Range (-∞,∞)
The function is continuous and increasing
The graph is concave down

5. Derivative of Natural Logs (ln)
General:
Chain Rule: Let u be a differentiable function of x such that
Absolute Value:

6. 2) Find the derivative of

7. Find the derivative of

8. 4.) Find the derivative of
rewrite
differentiate and simplify

9. 5) Find the derivative of

10. Find the derivative of

11. Solve using Logarithmic Differentiation
1. Take the ln of both sides
2. Use logarithmic properties
3. Differentiate
4. Solve for y’
5. Substitute for y
6. Simplify

12. 7) Find the derivative of

13. Remember
If y = ln(x), then
Therefore

14. Integration Rule for ln
Let u be a differentiable function in terms of x and du = u’dx

15. 8.) Find the antiderivative of

16. 9) Evaluate

17. 10) Evaluate

18. Home Work Derivatives and Integrals of logarithms worksheet 5-B
Use a section header for each of the topics, so there is a clear transition to the audience.
Derivatives and Integrals of logarithms
worksheet 5-B