1. Derivatives of Log Functions
Lesson 4.5

2. Problem Consider f(x) = logax
What if we try to use the definition for derivative using the limit
No way to break up this portion of the expression to let h → 0

3. Possible Solution We know that the derivative is the "slope function"
What if we graph y=ln(x) and check the slopes … plotting them

4. Slope Results
The table at the right shows the values of the slopes at various x values
What function might this be?
Appears to be x
slope of ln(x) at x
0.001
0.010
0.100
10.000
0.500
2.000
0.750
1.333
1.000
1.500
0.667
5.000
0.200

5. Derivative of the Log Function
For the natural logarithm ln(x)
For the log of a different base loga(x)

6. Examples Try these sample problems … find the derivative
Don't forget to use the chain rule where applicable

7. What About ln(-x)? Consider it a compound function
Apply the chain rule
Thus we see

8. Conclusion
We now can say
Apply to finding these derivatives

9. Assignment
Lesson 4.5
Page 289
Exercises 1 – 65 EOO