Q102 - mrbermel
Q104.AB.NOTES: Chapter 3.3, 3.5, 3.6
AB.Q104.LESSON 1 (3.3)
3.3 Techniques of Differentiation
Let [pic].
Notation for the derivative:
Lagrange:[pic]
Leibniz: [pic]
Newton: [pic]
Rules for the derivative
1. [pic]
2. [pic] (THE POWER RULE)
3. [pic]
4. [pic]
5. [pic] (THE PRODUCT RULE)
6. [pic] (THE QUOTIENT RULE)
LESSON 1: Examples
LESSON 1: Continued
1. Find the first three derivatives of the function. Use Lagrange and Leibniz notation.
2. Express each derivative using the appropriate properties.
3. Prove the Power Rule:
4. Prove the Product Rule:
LESSON1 – 3.3. HW: SEE THE PDF VERSION at
AB.Q104.Lesson 2 (3.5)
3.5: Derivatives of Trigonometric Functions
Important Limits: [pic] and [pic]
Important Identities: [pic] [pic]
1. Use the definition of derivative to find [pic]
2. Use the definition of derivative to find [pic]
3. Find [pic]
4. Find [pic]
~BOOK OF MEMORIES~
(ENTRY 1)
[pic]=
[pic]=
[pic]=
[pic]
[pic]
[pic]
LESSON 2: Examples
Ex: 1 Find [pic]if [pic]
Ex: 2 Find [pic]if [pic]
Ex: 3 Find [pic] if [pic]
LESSON 2: Examples Continued
LESSON2 – 3.5. HW: SEE THE PDF VERSION at
Additional HW Problems
1. Find [pic] (the 87th derivative of sin x)
2. Let [pic]. Find all positive integers n for which [pic].
3. Without using any trigonometric identity, find [pic].
4.Let [pic].
a) Find the x-coordinate of all points on the graph at which the tangent line is parallel to the line [pic]
b) Find an equation of the tangent line to the graph at the point on the graph with x-coordinate [pic].
AB.Q104.Lesson 3 (3.6)
Chapter 3.6 The Chain Rule
COMPOSITE FUNCTIONS REVIEW:
THE CHAIN RULE:
If [pic], [pic], and the derivatives [pic] and [pic] both exist, then the composite function defined by [pic] has a derivative given by [pic]
LESSON 3: Examples
LESSON 3: Examples Continued
LESSON 3: Notational Examples
LESSON3 – 3.6. HW: SEE THE PDF VERSION at
AB.Q104: LESSON 4 – NOTATIONAL EXAMPLES AND CHART EVALUATIONS
#1.
|[pic] |[pic] |[pic] |[pic] |[pic] |[pic] |[pic] |
|1 |-4 |5 |5 |8 |-1/2 |3 |
|2 |1 |3 |6 |-1 |0 |4 |
|6 |-10 |1/2 |3 |10 |3/2 |0 |
A. Find [pic] at [pic].
B. Find [pic] at [pic].
C. Find [pic]at [pic].
#2.
|[pic] |[pic] |[pic] |[pic] |[pic] |
|2 |8 |1/3 |2 |-3 |
|3 |3 |2( |-4 |5 |
A. Find [pic] at [pic]
B. Find [pic] at [pic]
C. Find [pic] at [pic]
D. Find [pic]at [pic]
#3.
|[pic] |[pic] |[pic] |[pic] |[pic] |
|0 |1 |5 |1 |1/3 |
|1 |3 |-1/3 |-4 |-8/3 |
A. Find [pic] at [pic]
B. Find [pic] at [pic]
C. Find [pic] at [pic]
D. Find [pic]at [pic]
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