1. Warm Up Sketch the graph of y = ln x What is the domain and range?
Determine the concavity of the graph.
Determine the intervals where the graph is increasing.
Evaluate each without using a calculator.
2) log ) ln e ) log

2. Homework Questions…

3. Derivatives involving ln and logb

4. Derivative involving natural logs.
“The derivative of ln of something is… one over the something times the derivative of the something.”

5. Examples
Find the derivative.

6. Find the derivative of y = x2 ln(x3)

7. Write the equation of the tangent line to y = ln (x1/2) at the point where x = 1

8. Sometimes it is easier to find a derivative if you use properties to simplify first.
Find the derivative of

9. Find the derivative of

10. Logarithmic Differentiation…
All it means is that you have something you want to differentiate, you take the natural log of both sides of an equation before you take the derivative.

11. Why would you want to do that?
Reason #1
Take the derivative of

12. Let’s Review the steps…
Take ln of both sides.
Simplify the right side using log properties.
Take the derivative of both sides.
(You always get on the left side)
4. Move the y to the right side of the = (to solve for dy/dx) and substitute the original y equation in for y.

13. Your Turn 
Use logarithmic differentiation to determine the derivative of

14. To determine the derivatives of logb (not ln), use the change of base formula to change it to ln.

15. Examples
Find the derivative.