Question 1

​Find the derivative of the function. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 2

​Find the third derivative of the function   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 3

Differentiate the given function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

Find the slope of the tangent line to the graph of the function below at the given point. ​   ,   ​

Accepted Answer

A)  ​4 
B)  ​-4 
C)  ​-2 
D)  ​6 
E)  ​none of the above 
A)  ​4 
B)  ​-4 
C)  ​-2 
D)  ​6 
E)  ​none of the above

Question 5

Find the slope of the tangent line to the graph of the function below at the given point. ​   ,   ​

Accepted Answer

A)  ​12 
B)  ​-3 
C)  ​-8 
D)  ​-12 
E)  ​none of the above 
A)  ​12 
B)  ​-3 
C)  ​-8 
D)  ​-12 
E)  ​none of the above

Question 6

​An airplane flying at an altitude of 4 miles passes directly over a radar antenna.When the airplane is 25 miles away   ,the radar detects that the distance s is changing at a rate of 220 miles per hour.What is the speed of the airplane? Round your answer to the nearest integer. ​

Accepted Answer

A)  ​223 mi/hr 
B)  ​​206 mi/hr 
C)  ​446​ mi/hr 
D)  ​​111 mi/hr 
E)  ​​103 mi/hr 
A)  ​223 mi/hr 
B)  ​​206 mi/hr 
C)  ​446​ mi/hr 
D)  ​​111 mi/hr 
E)  ​​103 mi/hr

Question 7

​Find the slope of the graph at the given point. ​   ​   ​

Accepted Answer

A)  ​2 
B)  ​0 
C)  ​1 
D)  ​3 
E)  ​5 
A)  ​2 
B)  ​0 
C)  ​1 
D)  ​3 
E)  ​5

Question 8

​Find the rate of change of x with respect to p. ​   ,   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 9

​Find the derivative of the function   State which differentiation rule(s)you used to find the derivative. ​

Accepted Answer

A)  ​1, Product Rule. 
B)  ​1, Quotient Rule. 
C)  ​5, Product Rule. 
D)  ​5, Quotient Rule. 
E)  ​   ,Product Rule. 
A)  ​1, Product Rule. 
B)  ​1, Quotient Rule. 
C)  ​5, Product Rule. 
D)  ​5, Quotient Rule. 
E)  ​   ,Product Rule.

Question 10

​Find   for the following equation: ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 11

You deposit $1,000 in an account with an annual interest rate of change r (in decimal form)compounded monthly.At the end of 4 years,the balance is   Find the rate of change of A with respect to r when   Round your answer to two decimal places. ​

Accepted Answer

A)  $1,375.67 
B)  $65,594.67 
C)  $114.64 
D)  $5,466.22 
E)  $5,430.02 
A)  $1,375.67 
B)  $65,594.67 
C)  $114.64 
D)  $5,466.22 
E)  $5,430.02

Question 12

​Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​
​   ,   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​both B and D 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​both B and D

Question 13

​Find the value   for the function   ​

Accepted Answer

A)  ​20,916 
B)  ​37,191 
C)  ​53,170 
D)  ​37,196 
E)  ​184,779 
A)  ​20,916 
B)  ​37,191 
C)  ​53,170 
D)  ​37,196 
E)  ​184,779

Question 14

Find   for the equation   by implicit differentiation and evaluate the derivative at the point   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  0 
A)    
B)    
C)    
D)    
E)  0

Question 15

​Find the derivative of the function. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​  
​ 
E)  ​none of the above 
A)  ​   
B)  ​   
C)  ​   
D)  ​  
​ 
E)  ​none of the above

Question 16

​Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​
​   ,   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above

Question 17

​Find the second derivative of the function. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​None of the above 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​None of the above

Question 18

​Find the derivative of the function   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 19

​Find the second derivative for the function   and solve the equation   ​

Accepted Answer

A)  ​0 
B)  ​4 
C)  ​-4 
D)  ​   
E)  ​no solution 
A)  ​0 
B)  ​4 
C)  ​-4 
D)  ​   
E)  ​no solution

Question 20

A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place. ​

Accepted Answer

A)  -24.1 feet/second 
B)  -0.2 feet/second 
C)  -0.6 feet/second 
D)  -15 feet/second 
E)  -0.9 feet/second 
A)  -24.1 feet/second 
B)  -0.2 feet/second 
C)  -0.6 feet/second 
D)  -15 feet/second 
E)  -0.9 feet/second

Find the derivative of the function.

Find the third derivative of the function

Differentiate the given function.

Find the slope of the tangent line to the graph of the function below at the given point. ,

Find the slope of the tangent line to the graph of the function below at the given point. ,

An airplane flying at an altitude of 4 miles passes directly over a radar antenna.When the airplane is 25 miles away ,the radar detects that the distance s is changing at a rate of 220 miles per hour.What is the speed of the airplane? Round your answer to the nearest integer.

Find the slope of the graph at the given point.

Find the rate of change of x with respect to p. ,

Find the derivative of the function State which differentiation rule(s)you used to find the derivative.

Find for the following equation:

You deposit $1,000 in an account with an annual interest rate of change r (in decimal form)compounded monthly.At the end of 4 years,the balance is Find the rate of change of A with respect to r when Round your answer to two decimal places.

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ,

Find the value for the function

Find for the equation by implicit differentiation and evaluate the derivative at the point

Find the derivative of the function.

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ,

Find the second derivative of the function.

Find the derivative of the function

Find the second derivative for the function and solve the equation

A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place.

Functions, graphs, and Limits

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 2: Differentiation

​Find the derivative of the function. ​ ​ ​

​Find the third derivative of the function ​

Differentiate the given function. ​ ​

Find the slope of the tangent line to the graph of the function below at the given point. ​ , ​

Find the slope of the tangent line to the graph of the function below at the given point. ​ , ​

​An airplane flying at an altitude of 4 miles passes directly over a radar antenna.When the airplane is 25 miles away ,the radar detects that the distance s is changing at a rate of 220 miles per hour.What is the speed of the airplane? Round your answer to the nearest integer. ​

​Find the slope of the graph at the given point. ​ ​ ​

​Find the rate of change of x with respect to p. ​ , ​

​Find the derivative of the function State which differentiation rule(s)you used to find the derivative. ​

​Find for the following equation: ​ ​

You deposit $1,000 in an account with an annual interest rate of change r (in decimal form)compounded monthly.At the end of 4 years,the balance is Find the rate of change of A with respect to r when Round your answer to two decimal places. ​

​Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​ ​ , ​

​Find the value for the function ​

Find for the equation by implicit differentiation and evaluate the derivative at the point ​

​Find the derivative of the function. ​ ​ ​

​Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​ ​ , ​

​Find the second derivative of the function. ​ ​

​Find the derivative of the function ​

​Find the second derivative for the function and solve the equation ​

A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place. ​

Functions, graphs, and Limits

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Find the derivative of the function.

Find the third derivative of the function

Differentiate the given function.

Find the slope of the tangent line to the graph of the function below at the given point. ,

Find the slope of the tangent line to the graph of the function below at the given point. ,

An airplane flying at an altitude of 4 miles passes directly over a radar antenna.When the airplane is 25 miles away ,the radar detects that the distance s is changing at a rate of 220 miles per hour.What is the speed of the airplane? Round your answer to the nearest integer.

Find the slope of the graph at the given point.

Find the rate of change of x with respect to p. ,

Find the derivative of the function State which differentiation rule(s)you used to find the derivative.

Find for the following equation:

You deposit $1,000 in an account with an annual interest rate of change r (in decimal form)compounded monthly.At the end of 4 years,the balance is Find the rate of change of A with respect to r when Round your answer to two decimal places.

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ,

Find the value for the function

Find for the equation by implicit differentiation and evaluate the derivative at the point

Find the derivative of the function.

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ,

Find the second derivative of the function.

Find the derivative of the function

Find the second derivative for the function and solve the equation

A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place.