Distributive Property 100

1
Limit Definition of Derivatives
Basic Rules
Product, Quotient, and Higher Order Derivatives
Chain Rule
Implicit Differentiation
100
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100
100
100
200
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200
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300
300
300
300
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400
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400
400
400
500
500
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500
Final Jeopardy
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Limit Definition of Derivatives 100
Use the limit definition for derivatives to find
the derivative of .
Get Answer
Main
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Limit Definition of Derivatives 100
If ,
Main
4
Limit Definition of Derivatives200
Use the limit definition for derivatives
to find the derivative of
at x 4.
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5
Limit Definition of Derivatives 200
If ,
Main
6
Limit Definition of Derivatives 300
Find the equation of the tangent line to
at x -3 by using the limit
definition of derivatives.
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7
Limit Definition of Derivatives300
If ,
Equation of Tangent Line at x -3
Main
8
Limit Definition of Derivatives 400
Get Answer
Main
9
Limit Definition of Derivatives 400
if .
Main
10
Limit Definition of Derivatives 500
If f (x) is continuous and differentiable at x
1. Find a and b.
Get Answer
Main
11
Limit Definition of Derivatives 500
If , If f
(x) is continuous and differentiable at x 1.
and .
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12
Basic Rules100
a) b) c)
d) e)
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13
Basic Rules 100
c)
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Basic Rules 200
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15
Basic Rules 200
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Basic Rules 300
Main
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17
Basic Rules 300
If ,
. At (2,16), .
Equation of Tangent Line at x 2
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18
Basic Rules 400
Find the tangent line of
at
MAY USE CALCULATOR
Main
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19
Basic Rules 400

• If ,
• and
• .

Equation of Tangent Line at x -3
Main
Main
20
Basic Rules 500
Find the equation of the line perpendicular to
the tangent line of at
.
Main
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21
Basic Rules 500

• If ,
• ,
• , and
• .

Equation of Tangent Line at x 1
Main
Main
Main
22
Product, Quotient, andHigher Order
Derivatives100
If , find
.
Main
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23
Product, Quotient, andHigher Order
Derivatives100
If ,
Main
24
Product, Quotient, andHigher Order
Derivatives200
Main
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25
Product, Quotient, andHigher Order
Derivatives200
Main
26
Product, Quotient, andHigher Order
Derivatives300
   
Find f (x) in its simplest form.
Main
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27
Product, Quotient, andHigher Order
Derivatives300
Find f (x) in its simplest form
Main
28
Product, Quotient, andHigher Order
Derivatives400
The position of a particle is given by
What is the acceleration of the particle at
Use a calculator!
Daily Double !
Main
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29
Product, Quotient, andHigher Order
Derivatives400
The position of a particle is given by
What is the acceleration of the particle at
Use a calculator!
Daily Double !
Main
30
Product, Quotient, andHigher Order
Derivatives500
Find do NOT use a CALCULATOR!
Main
Get Answer
31
Product, Quotient, andHigher Order
Derivatives500
Main
32
Chain Rule 100
Let f and u be differentiable functions of
x. Find
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33
Chain Rule 100
Let f and u be differentiable functions of x.
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Chain Rule 200
Differentiate .
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35
Chain Rule 200
Differentiate .
, .
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Chain Rule 300
Differentiate .
Daily Double !
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37
Chain Rule 300
Differentiate .
Daily Double !
Main
38
Chain Rule 400
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39
Chain Rule 400
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Chain Rule 500
Suppose that functions f and g have the
following values.
What is the value of the derivative of
at ?
Main
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41
Chain Rule 500
Suppose that functions f and g have the
following values.
What is the value of the derivative of
at ?
Main
42
Implicit Differentiation100
Find
Main
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43
Implicit Differentiation100
Find

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44
Implicit Differentiation200
Find
Main
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45
Implicit Differentiation200
Find


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Implicit Differentiation300
Find in its simplest form.
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47
Implicit Differentiation300
Find in its simplest form.
Main
48
Implicit Differentiation 400
Find the slope of the tangent line when x 1
and y 3.
Main
Get Answer
49
Implicit Differentiation 400
Find the slope of the tangent line when x 1
and y 3.
Main
Main
50
Implicit Differentiation500
Find the slope of the tangent line when x 2.
Main
Get Answer
51
Implicit Differentiation 500
Find the slope of the tangent line when x 2.
Main
52
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53
A Patrol Car is parked 50 feet from a long
warehouse. The revolving light on top of the car
turns at a rate of 30 revolutions per minute. How
fast is the light beam moving along the wall (in
ft/sec) when the beam makes an angle of
?
54
A Patrol Car is parked 50 feet from a long
warehouse. The revolving light on top of the car
turns at a rate of 30 revolutions per minute. How
fast is the light beam moving along the wall (in
ft/sec) when the beam makes an angle of
?
Remember