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. Song about the Power Rule
5. Higher-Order Derivatives (Second derivatives, ...)
To determine the second derivative, take the derivative of the first derivative.
The notation for the second derivative:
Examples:
