1. Differentiation Rules (Constant, Power, Sum, Difference)
AP Calculus
October 3, 2016
Mrs. Agnew

2. Essential Question Essential Vocabulary
How can we find the derivative of a function quickly and efficiently?
Essential Vocabulary
Constant Rule
Power Rule
Constant Multiple Rule
Sum/Difference Rule
Positive-Velocity-Acceleration Problems

3. Basic Rules The Constant Rule: The derivative of a constant is zero.
The Linear Rule: The derivative of a linear function is the slope.

4. The Power Rule Given f(x) = xn, then… Guided Practice…
Including negative exponents, rational exponents, and radicals

5. Constant Multiple Rule
The derivative of a constant times a function is equal to the constant times the derivative of the function.
Guided Practice…

6. Sum & Difference Rules
The use of these rules, along with the power rule, makes finding the derivative of polynomials easy.

7. The Second Derivative
The second derivative of a function is the “derivative of the derivative.”
Notations for second derivative:

8. P-V-A Problems Given a function that gives the position
of an object at any time t, the velocity and acceleration of the object are found by:
Velocity:
Acceleration:

9. Guided Practice
Find tangent lines to curves and horizontal tangent lines
Find second derivatives
P-V-A problems
Application Problems…

10. Homework:
Page 115 – 118 #15, 17, 35, 39 – 51 (Odd), 59, 61, 80, 87 – 92, 95, 117