Lesson #23
Rules for Differentiation
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Quote of the Day:
"Although I am absolutely without training or
knowledge in the exact sciences, I often seem
to have more in common with mathematicians
than with my fellow artists." -- M.C. Escher
Objectives:
The student will prove the power rule for derivatives.
The student will apply the appropriate derivative
formula to solving derivative problems.
1. Collect Homework.
2. Rules for Derivatives:
Rule #1: Definition of the Derivative
Rule #2: The derivative of a constant is zero.
If f(x) = k
Then f'(x) = 0.
Draw a diagram to see this (interpret the
derivative as slope).
Rule #3: The Power Rule
Proof:
Rule #4: The Sum Rule 
Proof:
Rule #5: The Difference Rule 
The proof is similar to the proof of the Sum Rule.
3. Examples:
4. Comic Strip about the Definition of the Derivative 5. Comic Strip regarding the Binomial Expansion
6. Higher-Order Derivatives (Second derivatives, …)
To determine the second derivative, take the
derivative of the first derivative.
The notation for the second derivative:
Examples:
7. Assignment:
p. 196 (1, 3, 5, 9, 13, 15, 21, 37a,c, 39, 41a,b, 57)
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