تكلم مع الذكاء الاصطناعي
Deck 3: Section 3: Differentiation
ملء الشاشة (f)
سؤال
Find the derivative of the algebraic function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Use the Product Rule to differentiate. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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
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 secondB)
cubic inches per secondC)
cubic inches per secondD)
cubic inches per secondE)
cubic inches per second سؤال
Use the Product Rule to differentiate 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Use the Quotient Rule to differentiate the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Use the Quotient Rule to differentiate the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Find an equation of the tangent line to the graph of f at the given point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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
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/secondB)
square inches/secondC)
square inches/secondD)
square inches/secondE)
square inches/second سؤال
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.
A)
B)
C)
D)
E) The graph has no horizontal tangents.
سؤال
Find the derivative of the function. 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Find the derivative of the function 
. Simplify your answer.
A)
B)
C)
D)
E)
. Simplify your answer.A)
B)
C)
D)
E)
سؤال
Use the Product Rule to differentiate 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Use the quotient rule to differentiate the following function 
and evaluate 
.
A)
B)
C)
D)
E)
and evaluate .A)
B)
C)
D)
E)
سؤال
Find the derivative of the algebraic function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Use the Quotient Rule to differentiate the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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.
A) -6.44 thousand dollars per hundred
B) 8.04 thousand dollars per hundred
C) 3.28 thousand dollars per hundred
D) -4.92 thousand dollars per hundred
E) -7.96 thousand dollars per hundred
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.A) -6.44 thousand dollars per hundred
B) 8.04 thousand dollars per hundred
C) 3.28 thousand dollars per hundred
D) -4.92 thousand dollars per hundred
E) -7.96 thousand dollars per hundred
سؤال
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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.
A) 226.7 bacteria per hour
B) 68.89 bacteria per hour
C) 65.26 bacteria per hour
D) 51.52 bacteria per hour
E) 61.23 bacteria per hour
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.A) 226.7 bacteria per hour
B) 68.89 bacteria per hour
C) 65.26 bacteria per hour
D) 51.52 bacteria per hour
E) 61.23 bacteria per hour
سؤال
Find the derivative of the trigonometric function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Find the second derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Find the second derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Given the derivative below find the requested higher-order derivative. 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Find the second derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
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.
A) 1.9 ft/sec2
B) 0.9 ft/sec2
C) 0.6 ft/sec2
D) 0.2 ft/sec2
E) 8.3 ft/sec2
where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.A) 1.9 ft/sec2
B) 0.9 ft/sec2
C) 0.6 ft/sec2
D) 0.2 ft/sec2
E) 8.3 ft/sec2
سؤال
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. 
A) -2973 mi/radian
B) -5150 mi/radian
C) 5150 mi/radian
D) -8920 mi/radian
E) 2973 mi/radian
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. A) -2973 mi/radian
B) -5150 mi/radian
C) 5150 mi/radian
D) -8920 mi/radian
E) 2973 mi/radian
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العب
ملء الشاشة (f)
Deck 3: Section 3: Differentiation
1
Find the derivative of the algebraic function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
2
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
3
Use the Product Rule to differentiate.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
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
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 secondB)
cubic inches per secondC)
cubic inches per secondD)
cubic inches per secondE)
cubic inches per second فتح الحزمة
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5
Use the Product Rule to differentiate .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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6
Use the Quotient Rule to differentiate the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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7
Use the Quotient Rule to differentiate the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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8
Find an equation of the tangent line to the graph of f at the given point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
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
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/secondB)
square inches/secondC)
square inches/secondD)
square inches/secondE)
square inches/second فتح الحزمة
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10
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.
A)
B)
C)
D)
E) The graph has no horizontal tangents.
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11
Find the derivative of the function. .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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12
Find the derivative of the function . Simplify your answer.
A)
B)
C)
D)
E)
. Simplify your answer.A)
B)
C)
D)
E)
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13
Use the Product Rule to differentiate .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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14
Use the quotient rule to differentiate the following function and evaluate .
A)
B)
C)
D)
E)
and evaluate .A)
B)
C)
D)
E)
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15
Find the derivative of the algebraic function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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16
Use the Quotient Rule to differentiate the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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17
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.
A) -6.44 thousand dollars per hundred
B) 8.04 thousand dollars per hundred
C) 3.28 thousand dollars per hundred
D) -4.92 thousand dollars per hundred
E) -7.96 thousand dollars per hundred
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.A) -6.44 thousand dollars per hundred
B) 8.04 thousand dollars per hundred
C) 3.28 thousand dollars per hundred
D) -4.92 thousand dollars per hundred
E) -7.96 thousand dollars per hundred
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18
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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19
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.
A) 226.7 bacteria per hour
B) 68.89 bacteria per hour
C) 65.26 bacteria per hour
D) 51.52 bacteria per hour
E) 61.23 bacteria per hour
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.A) 226.7 bacteria per hour
B) 68.89 bacteria per hour
C) 65.26 bacteria per hour
D) 51.52 bacteria per hour
E) 61.23 bacteria per hour
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20
Find the derivative of the trigonometric function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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21
Find the second derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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22
Find the second derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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23
Given the derivative below find the requested higher-order derivative. .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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24
Find the second derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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25
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.
A) 1.9 ft/sec2
B) 0.9 ft/sec2
C) 0.6 ft/sec2
D) 0.2 ft/sec2
E) 8.3 ft/sec2
where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.A) 1.9 ft/sec2
B) 0.9 ft/sec2
C) 0.6 ft/sec2
D) 0.2 ft/sec2
E) 8.3 ft/sec2
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26
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.
A) -2973 mi/radian
B) -5150 mi/radian
C) 5150 mi/radian
D) -8920 mi/radian
E) 2973 mi/radian
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. A) -2973 mi/radian
B) -5150 mi/radian
C) 5150 mi/radian
D) -8920 mi/radian
E) 2973 mi/radian
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