Question 1

Find the derivative of the function   . ​

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Question 2

Find   by implicit differentiation given that   . ​​

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Question 3

Assume that x and y are both differentiable functions of t.Find   when   and   for the equation   . ​

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Question 4

Find the derivative of the function. ​   ​

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Question 5

Find the derivative of the algebraic function   .

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Question 6

Find the derivative of the function. ​   ​

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Question 7

When satellites observe Earth,they can scan only part of Earth's surface.Some satellites have sensors that can measure the angle θ 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 θ when   (Assume r = 3960 miles. )Round your answer to the nearest unit. ​   ​

Accepted Answer

A) -13718   
B) -7920   
C) 7920   
D) -4573   
E) 13718   
A) -13718   
B) -7920   
C) 7920   
D) -4573   
E) 13718

Question 8

Find the derivative of the function   . ​

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Question 9

Use the rules of differentiation to find the derivative of the function   . ​

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Question 10

Find the slope of the graph of the function at the given value. ​   when   ​

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Question 11

Find the derivative of the function. ​   ​

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Question 12

Find the slope-intercept form of the equation of the line tangent to the graph of   when   . ​

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Question 13

Given the derivative below find the requested higher-order derivative. ​   ,   .
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Question 14

Find   if   . ​

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Question 15

Evaluate the derivative of the function   at the point   . ​

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Question 16

A ladder a = 20 feet long is leaning against the wall of a house (see figure).The base of the ladder is pulled away from the wall at a rate of b = 4 feet per second.Consider the triangle formed by the side of the house,the ladder,and the ground.Find the rate at which the area of the triangle is changed when the base of the ladder is 11 feet from the wall.Round your answer to two decimal places. ​   ​

Accepted Answer

A) 1.48   
B) 33.41   
C) 153.81   
D) 18.92   
E) 53.68   
A) 1.48   
B) 33.41   
C) 153.81   
D) 18.92   
E) 53.68

Question 17

Find the slope of the graph of the function at the given value. ​   when   ​
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Question 18

Use the Quotient Rule to differentiate the function   . ​

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Question 19

Find the derivative of the function. ​   ​

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Question 20

Find an equation of the tangent line to the graph of the function   at the point   . ​

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Find the derivative of the function .

Find by implicit differentiation given that .

Assume that x and y are both differentiable functions of t.Find when and for the equation .

Find the derivative of the function.

Find the derivative of the algebraic function .

Find the derivative of the function.

Find the derivative of the function .

Use the rules of differentiation to find the derivative of the function .

Find the slope of the graph of the function at the given value. when

Find the derivative of the function.

Find the slope-intercept form of the equation of the line tangent to the graph of when .

Given the derivative below find the requested higher-order derivative. , .

Find if .

Evaluate the derivative of the function at the point .

Find the slope of the graph of the function at the given value. when

Use the Quotient Rule to differentiate the function .

Find the derivative of the function.

Find an equation of the tangent line to the graph of the function at the point .

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 3: Differentiation

Find the derivative of the function . ​

Find by implicit differentiation given that . ​​

Assume that x and y are both differentiable functions of t.Find when and for the equation . ​

Find the derivative of the function. ​ ​

Find the derivative of the algebraic function .

Find the derivative of the function. ​ ​

Find the derivative of the function . ​

Use the rules of differentiation to find the derivative of the function . ​

Find the slope of the graph of the function at the given value. ​ when ​

Find the derivative of the function. ​ ​

Find the slope-intercept form of the equation of the line tangent to the graph of when . ​

Given the derivative below find the requested higher-order derivative. ​ , . ​

Find if . ​

Evaluate the derivative of the function at the point . ​

Find the slope of the graph of the function at the given value. ​ when ​ ​

Use the Quotient Rule to differentiate the function . ​

Find the derivative of the function. ​ ​

Find an equation of the tangent line to the graph of the function at the point . ​

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find the derivative of the function .

Find by implicit differentiation given that .

Assume that x and y are both differentiable functions of t.Find when and for the equation .

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the function .

Use the rules of differentiation to find the derivative of the function .

Find the slope of the graph of the function at the given value. when

Find the derivative of the function.

Find the slope-intercept form of the equation of the line tangent to the graph of when .

Given the derivative below find the requested higher-order derivative. , .

Find if .

Evaluate the derivative of the function at the point .

Find the slope of the graph of the function at the given value. when

Use the Quotient Rule to differentiate the function .

Find the derivative of the function.

Find an equation of the tangent line to the graph of the function at the point .