Quote of the Day: 
"Who has not been amazed to learn that the function y = e^x, like a 
      phoenix rising from its own ashes, is its own derivative?" 
           -- Francois le Lionnais

Objectives:
The student will take derivatives of logarithms to any base. 
     
1. Bell Ringer.  

2. Develop the derivative formula for 

3. So,

4. Examples

5. Develop the formula for the derivative of a^u

6. Examples:

7. Emphasize the differences between the derivatives of the
   various exponential functions: 

8. Proofs of the derivative of a variable to a variable
        Click here to see the proofs -- ONLY after you tried it yourself!

9. Jokes – e^x

There's an old MIT football cheer: 
E to the x, dy, dx, 
E to the x, dx.
Secant, tangent, cosine, sine,
3.14159. 
Square root, cube root, log base e, 
Cheers for math at MIT. 

------------------------------------------------

A mathematician went insane and believed that he was 
the differentiation operator. 
His friends had him placed in a mental hospital 
until he got better. 
All day he would go around frightening the other patients 
by staring at them and saying "I differentiate you!" 
One day he met a new patient; 
and true to form he stared at him and said "I differentiate you!", 
but for once, his victim's expression didn't change. 

Surprised, the mathematician marshalled his energies, 
stared fiercely at the new patient and said loudly 
"I differentiate you!", but still the other man had no reaction. 
Finally, in frustration, the mathematician screamed out 
"I DIFFERENTIATE YOU!" 

The new patient calmly looked up and said, 
"You can differentiate me all you like: I'm e to the x." 


10. Assignment: 
      p. 254 (11, 13, 15, 17, 22, 23, 27, 31)  

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