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 functions involving exponents:
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.
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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 marshaled 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."