1. 4-4 Delicious derivatives of Exponential & logarithmic functions

2. Derivative of e x
Ex 1) Find

3. Derivative of a x
Mini Proof

4. Ex 2) At what point on the graph of the function y = 2t – 3
does the tangent line have a slope of 21?
deriv
(4.921, )

5. Derivative of ln x
Mini Proof

6. Ex 3) A line with slope m passes through the origin and is tangent to the graph of y = ln x. What is the value of m?
(0, 0) and (a, ln a)
m = x = a
same slope:

7. Derivative of log a x
change of base
Mini Proof

8. Power Rule (Reminder):
*Now we will have any real # as our exponent*
Ex 5a) Find
b) Find

9. Ex 6) If f (x) = ln (x – 3), find f '(x).
State the domain of f '(x).
Domain? Thinking x  3
BUT domain of f ?  Can’t have ln of a neg #
so domain of f : x – 3 > 0  (3, )
So domain of f '(x) is (3, ) also

10. Ex 8) Spread of flu modeled by equation
a) Estimate the initial number of students infected with the flu.
b) How fast is the flu spreading after 3 days?
Need slope  derivative evaluated at t = 3

11. Ex 8) Spread of flu modeled by equation
c) When will the flu spread at its maximum rate? What is this rate?
Graph the derivative & find max
2nd Trace (CALC)  4: Max
x =  3 days
Rate? From part b  25 students/day
(Zoom  0: zoomfit)

12. homework
Pg #1, 10, 16, 20, 35, 39
Pg #1 – 41 (skip mult of 3), 49, 51