Warm-up 8/31

Compute several different ways . How many different ways can you find?

Finding the derivative and calculating the derivative at a value

calculating the derivative at a value using the graph

On the graph screen F5

Pick a value to differentiate say x = 2

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.

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

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**

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

2( )

( ) sin

f x x

g x x

( )f g x 2 sin x

2sin x

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

32 siny x x

'y

inside

outside

23 2 sinx x 2 cosx x

4

7

2 3y

t

'y 528

2 3t 2

47 2 3t

2 4

xy

x

'y 2 4x 1 x

12 21

42x

2x

22 4x

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

3tan 9y x

'y 23 tan 9x 9

3tan 9x

2sec 9x

2 5 2(( 3) )y x x

'y

Simplifying Derivatives

techniques to simplifying the “raw derivatives”

Simplifying by Factoring Out the Least Powers

Find the derivative of

Solution:

Simplifying the Derivative of a Quotient

Simplifying the Derivative of a Power