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Warm-up 8/31
Compute several different ways . How many different ways can you find?
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Finding the derivative and calculating the derivative at a value
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calculating the derivative at a value using the graph
On the graph screen F5
Pick a value to differentiate say x = 2
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Homework Group
Check in with your group!
See which problems you have questions on
Help your group member.
Still unsure ? Thank about what you need to ask. Write those questions down.
- Go over as a class.
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Be seated before the bell rings
DESK
homeworkWarm-up (in your notes)
Agenda : warm-up / go over hwHw Quiz
Notes lesson 2.4 the chain rule
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NotebookTable of content
Page1
Learning Target 1
2) 1-2 Finding limits graphically and numerically
3) 1-3 Evaluating limits analytically
4) 1-4 Continuity
5) 1-5 & 3.5
6) 2.1 The Derivative
7)2.2 The power rule
8) 2.3 The Product Rule/quotient rule
9)2.4 chain rule
Learning Target
LT2: I can use the chain rule
HW:p 136; 1-6,7-21odd,23*,25*,43-63 odd,73a,74a,102**
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2.4 The chain rule2( ) 2f x x x
( ) 3 7g x x
2 2 3 7x 3 7x
inside
Outside
( ) ( )f x g x
( ) ( )f x g x
( )
( )
f x
g x
( )f g x
( ) cos
( ) 9
f x x
g x x
( )f g x cos9x
( ( ))f g x
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2( )
( ) sin
f x x
g x x
( )f g x 2 sin x
2sin x
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2.4 The chain rule
5 23y x x
1/2 y 5 23x x
Operation is Multiplication
1/21' 2y
5 23x x 45 6x x
.
der outside
.
der inside
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32 siny x x
'y
inside
outside
23 2 sinx x 2 cosx x
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4
7
2 3y
t
'y 528
2 3t 2
47 2 3t
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2 4
xy
x
'y 2 4x 1 x
12 21
42x
2x
22 4x
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sin 2y x 2siny x2siny x
' cos 2 2y x
' 2cos 2y x
2' cos 2y x x
' 2 cos 2y x x
' 2 sin cosy x x
' 2sin cosy x x
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3tan 9y x
'y 23 tan 9x 9
3tan 9x
2sec 9x
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2 5 2(( 3) )y x x
'y
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Simplifying Derivatives
techniques to simplifying the “raw derivatives”
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Simplifying by Factoring Out the Least Powers
Find the derivative of
Solution:
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Simplifying the Derivative of a Quotient
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Simplifying the Derivative of a Power