3.3 Product and Quotient Rules and Higher-Order Derivatives
129
____ 4.
Use the Quotient Rule to differentiate the function
.
a.
b.
c.
d.
e.
130
Chapter 3: Differentiation
____
5.
.
a.
b.
c.
d.
e.
3.3 Product and Quotient Rules and Higher-Order Derivatives
131
____
6.
Use the quotient rule to differentiate the following function
and
evaluate
.
a.
b.
c.
d.
e.
____
7.
Find the derivative of the algebraic function
.
a.
b.
c.
d.
e.
132 Chapter 3: Differentiation
____ 8. Use the Product Rule to differentiate .
a.
b.
c.
d.
e.
____ 9. Use the Product Rule to differentiate.
a.
b.
c.
d.
e.
3.3 Product and Quotient Rules and Higher-Order Derivatives
133
____
10.
Use the Quotient Rule to differentiate the function
.
a.
b.
c.
d.
e.
____
11.
Find the derivative of the function
.
a.
b.
c.
d.
e.
134
Chapter 3: Differentiation
____
12.
Find the derivative of the function
. Simplify your answer.
a.
b.
c.
d.
e.
____ 13. Find the derivative of the function.
.
a.
b.
c.
d.
e.
____ 14. Find the derivative of the trigonometric function .
a.
b.
c.
d.
e.
3.3 Product and Quotient Rules and Higher-Order Derivatives
135
____ 15.
Find an equation of the tangent line to the graph of f at the given point.
a.
b.
c.
d.
e.
____ 16. Determine all values of x, (if any), at which the graph of the function has a horizontal
tangent.
a.
b.
c.
d.
e. The graph has no horizontal tangents.
____ 17. The length of a rectangle is and its height is , where t is time in seconds and
the dimensions are in inches. Find the rate of change of area, A, with respect to time.
a.
square inches/second
b.
square inches/second
c.
square inches/second
d.
square inches/second
e.
square inches/second
136
Chapter 3: Differentiation
____
18.
The radius of a right circular cylinder is
and its height is , where t is
time in seconds and the dimensions are in inches. Find the rate of change of the volume of the
cylinder, V, with respect to time.
a.
cubic inches per second
b.
cubic inches per second
c.
cubic inches per second
d.
cubic inches per second
e.
cubic inches per second
____
19.
The ordering and transportation cost C for the components used in manufacturing a
product is
where C is measured in thousands of dollars and x is the
order size in hundreds. Find the rate of change of C with respect to x for x = 24. Round your
answer to two decimal places.
–6.44 thousand dollars per hundred
8.04 thousand dollars per hundred
3.28 thousand dollars per hundred
–4.92 thousand dollars per hundred
–7.96 thousand dollars per hundred
____ 20.
A population of 620 bacteria is introduced into a culture and grows in number
according to the equation
where t is measured in hours. Find the rate at
which the population is growing when t = 2. Round your answer to two decimal places.
226.7 bacteria per hour
68.89 bacteria per hour
65.26 bacteria per hour
51.52 bacteria per hour
61.23 bacteria per hour
3.3 Product and Quotient Rules and Higher-Order Derivatives
137
____ 21.
When satellites observe Earth, they can scan only part of Earth‘s surface. Some
satellites have sensors that can measure the angle
shown in the figure. Let h represent the satellite‘s
distance from Earth’s surface and let r represent Earth’s radius. Find the rate at which h is changing
with respect to when (Assume r = 4460 miles.) Round your answer to the nearest unit.
–2973 mi/radian
–5150 mi/radian
5150 mi/radian
–8920 mi/radian
2973 mi/radian
____ 22. Find the second derivative of the function .
a.
b.
c.
d.
e.
138
Chapter 3: Differentiation
____
23.
Find the second derivative of the function
.
a.
b.
c.
d.
e.
____
24.
Find the second derivative of the function
.
a.
b.
c.
d.
e.
____
25.
Given the derivative below find the requested higher-order derivative.
.
a.
b.
c.
d.
e.
3.3 Product and Quotient Rules and Higher-Order Derivatives
139
____ 26.
Suppose that an automobile‘s velocity starting from rest is
where v is
measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one
decimal place.
1.9 ft/sec2
0.9 ft/sec2
0.6 ft/sec2
0.2 ft/sec2
8.3 ft/sec2
140 Chapter 3: Differentiation
3.3 Product and Quotient Rules and Higher-Order Derivatives
Answer Section
3.3 Product and Quotient Rules and Higher-Order Derivatives
141
142 Chapter 3: Differentiation
3.4 The Chain Rule
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1.
Find the derivative of the algebraic function
.
a.
b.
c.
d.
e.
____
2.
Find the derivative of the function.
a.
b.
c.
d.
e.
____ 3. Find the derivative of the function.
a.
b.
c.
d.
e.
3.4 The Chain Rule
143
____ 4. Find the derivative of the function.
a.
b.
c.
d.
e.
____ 5. Find the derivative of the function.
a.
b.
c.
d.
e.
144 Chapter 3: Differentiation
____ 6. Find the derivative of the function.
a.
b.
c.
d.
e.
____ 7. Find the derivative of the function .
a.
b.
c.
d.
e.
____ 8. Find the derivative of the function .
a.
b.
c.
d.
e.
3.4 The Chain Rule
145
____ 9. Find the derivative of the function.
a.
b.
c.
d.
e.
____ 10. Find the derivative of the function.
a.
b.
c.
d.
e.
____ 11. Differentiate the function .
a.
b.
c.
d.
e.
146
Chapter 3: Differentiation
____
12.
Find the derivative of the function
.
a.
b.
c.
d.
e.
____
13.
Find
if
.
a.
b.
c.
d.
e.
____
14.
Differentiate the function
.
a.
b.
c.
d.
e.
3.4 The Chain Rule
147
____ 15.
Find the derivative of the function
. Simplify your answer.
a.
b.
c.
d.
e.
____ 16. Find the derivative of the function .
a.
b.
c.
d.
e.
____ 17. Find if .
a.
b.
c.
d.
e.
148
Chapter 3: Differentiation
____
18.
Find the derivative of the function
. Simplify your answer.
a.
b.
c.
d.
e.
____
19.
Find the derivative of the function
. Simplify your answer.
a.
b.
c.
d.
e.
____
20.
Differentiate the function
.
a.
b.
c.
d.
e.