# Section_ 2.4 The Chain Rule

Education

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Q 1

Find the derivative of the algebraic function .
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C

Q 2

Find the derivative of the function.
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B

Q 3

Find the derivative of the function.
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A

Q 4

Find the derivative of the function.
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Q 5

Find the derivative of the function.
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Q 6

Find the derivative of the function.
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Q 7

Find the derivative of the function .
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Q 8

Find the derivative of the function .
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Q 9

Find the derivative of the function.
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Q 10

Find the derivative of the function.
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Q 11

Differentiate the function .
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Q 12

Find the derivative of the function .
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Q 13

Find if .
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Q 14

Differentiate the function .
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Q 15

Find the derivative of the function .Simplify your answer.
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Q 16

Find the derivative of the function .
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Q 17

Find if .
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Q 18

Find the derivative of the function .Simplify your answer.
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Q 19

Find the derivative of the function .Simplify your answer.
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Q 20

Differentiate the function .
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Q 21

Find the derivative of the function .
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Q 22

Find the derivative of the function .
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Q 23

Find the derivative of the function .
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Q 24

Find the second derivative of the function.
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Q 25

Find the second derivative of the function .
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Q 26

Find if .
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Q 27

Evaluate the derivative of the function at the point .
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Q 28

Evaluate the derivative of the function at the given point. ,
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Q 29

Evaluate the derivative of the function at the point .
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Q 30

Evaluate the derivative of the function at the point .
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Q 31

Find an equation to the tangent line for the graph of f at the given point. ,
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Q 32

Find an equation to the tangent line to the graph of the function at the point .The coefficients below are given to two decimal places.
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Q 33

Find an equation of the tangent line to the graph of at the point (1,0).
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Q 34

Find an equation of the tangent line to the graph of at the point (0,1).
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Q 35

Find if .
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Q 36

Find if .
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Q 37

Find if .
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Q 38

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds.Determine the position of the object when .Round your answer to two decimal places.
A)2.18 feet
B)0.84 feet
C)3.82 feet
D)0.69 feet
E)0.34 feet

Multiple Choice

Q 39

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds.Determine the velocity of the object when .Round your answer to two decimal places.
A)5.46 ft/sec
B)2.40 ft/sec
C)3.46 ft/sec
D)4.46 ft/sec
E)0.87 ft/sec

Multiple Choice

Q 40

Suppose a 27-centimeter pendulum moves according to the equation where θ is the angular displacement from the vertical in radians and t is the time in seconds.Determine the rate of change of θ when t = 7 seconds.Round your answer to four decimal places.
A)2.9207 radians per second
B)4.0358 radians per second
C)0.6416 radians per second
D)2.7593 radians per second
E)5.4991 radians per second

Multiple Choice

Q 41

A buoy oscillates in simple harmonic motion as waves move past it.The buoy moves a total of 12.5 feet (vertically)between its low point and its high point.It returns to its high point every 8 seconds.Write an equation describing the motion of the buoy if it is at its high point at .
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Q 42

A buoy oscillates in simple harmonic motion as waves move past it.The buoy moves a total of 11.5 feet (vertically)between its low point and its high point.It returns to its high point every 10 seconds.Determine the velocity of the buoy as a function of t.
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Q 43

If the annual rate of inflation averages 7% over the next 10 years,the approximate cost C of goods or services during any year in that decade is where t is the time in years and P is the present cost.The price of an oil change for your car is presently $25.45.Estimate the price 8 years from now.Round your answer to two decimal places.
A)$27.23
B)$43.73
C)$217.85
D)$27.17
E)$255.37

Multiple Choice

Q 44

If the annual rate of inflation averages 4% over the next 10 years,the approximate cost C of goods or services during any year in that decade is where t is the time in years and P is the present cost.The price of an oil change for your car is presently $24.75.Find the rate of change of C with respect to t when .Round your answer to three decimal places.
A)38.101 dollars per year
B)1.010 dollars per year
C)1.437 dollars per year
D)10.644 dollars per year
E)84.358 dollars per year

Multiple Choice