Question 1

Find   where f(x) = sin 6 5x.

Accepted Answer

Question 2

Use the definition of the derivative to calculate f '(x) if f(x) = 2x2 - 2x and find the equation of the tangent line and the normal line to the graph of f at x = 2.

Accepted Answer

f '(x) = 4x¹

Question 3

Find the instantaneous rate of change of y = 3x2 with respect to x at x0 = 5.

Accepted Answer

A)  6 
B)  30 
C)  10 
D)  15 
E)  16 
A)  6 
B)  30 
C)  10 
D)  15 
E)  16

Question 4

Find f '(x) if f(x) = x sin x.

Accepted Answer

The answer of Find f '(x) if f(x) = x...

Question 5

Answer true or false. The derivative of the function graphed on the left is graphed on the right.

Accepted Answer

A) True 
 B)False

Question 6

Let   . Find the instantaneous rate of change of y with respect to x at the point x = 5.

Accepted Answer

The answer of Let   . Find the instantaneous...

Question 7

Find f '(x) if f(x) = x tan x.

Accepted Answer

x sec<sup>

Question 8

Let f(x) = 3x2. Find the slope of the tangent to the graph of f at a general point x0 using limits and find the slope of the tangent at x0 = 3.

Accepted Answer

@#IMG-DLM& Slope of

Question 9

f(x) = sin(6x). f'(x) =

Accepted Answer

A)  6 cos(6x) 
B)  cos(6x) 
C)  6 cos(x) 
D)  6 sin(6x) 
E)  sin(6x) 
A)  6 cos(6x) 
B)  cos(6x) 
C)  6 cos(x) 
D)  6 sin(6x) 
E)  sin(6x)

Question 10

Find equations for the tangent and normal lines to the graph of f(x) = cos(4 - x2) at x = 2.

Accepted Answer

Tangent: y

Question 11

Find dy/dx if y = 5x8.

Accepted Answer

A)  40x8 
B)  5x7 
C)  40x7 
D)  40x 
E)  x7 
A)  40x8 
B)  5x7 
C)  40x7 
D)  40x 
E)  x7

Question 12

Use the definition of the derivative to calculate f '(x) if f(x) = 4x4 + 7 and find the equations of the tangent line and the normal line to the graph of f at x = -4.

Accepted Answer

Derivative: y = 16x<

Question 13

Find the equation of the tangent line to   at x = 8.

Accepted Answer

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

Question 14

Answer true or false. If x is given in radians, the derivative formula for y = sin x in degrees is   .

Accepted Answer

A) True 
 B)False

Question 15

Answer true or false. If   ,   .

Accepted Answer

A) True 
 B)False

Question 16

The cost of manufacturing an object is given by C = f(x) dollars. Estimate the cost of making the 310th item if f '(309) = $74.

Accepted Answer

The answer of The cost of manufacturing an object is...

Question 17

Let   . Use the definition of the derivative to find   .

Accepted Answer

The answer of Let   . Use the definition...

Question 18

Answer true or false. If   ,   .

Accepted Answer

A) True 
 B)False

Question 19

Let f(x) = sin x. Estimate   by using a graphing utility.

Accepted Answer

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

Question 20

Find   , if   .

Accepted Answer

A)  30x5 
B)  6x5 - 6 
C)    
D)  5x5 
E)    
A)  30x5 
B)  6x5 - 6 
C)    
D)  5x5 
E)

Find where f(x) = sin ⁶ 5x.

Use the definition of the derivative to calculate f '(x) if f(x) = 2x² - 2x and find the equation of the tangent line and the normal line to the graph of f at x = 2.

Find the instantaneous rate of change of y = 3x² with respect to x at x₀ = 5.

Find f '(x) if f(x) = x sin x.

Answer true or false. The derivative of the function graphed on the left is graphed on the right.

Let . Find the instantaneous rate of change of y with respect to x at the point x = 5.

Find f '(x) if f(x) = x tan x.

Let f(x) = 3x². Find the slope of the tangent to the graph of f at a general point x₀ using limits and find the slope of the tangent at x₀ = 3.

f(x) = sin(6x). f'(x) =

Find equations for the tangent and normal lines to the graph of f(x) = cos(4 - x²) at x = 2.

Find dy/dx if y = 5x⁸.

Use the definition of the derivative to calculate f '(x) if f(x) = 4x⁴ + 7 and find the equations of the tangent line and the normal line to the graph of f at x = -4.

Find the equation of the tangent line to at x = 8.

Answer true or false. If x is given in radians, the derivative formula for y = sin x in degrees is .

Answer true or false. If , .

The cost of manufacturing an object is given by C = f(x) dollars. Estimate the cost of making the 310^th item if f '(309) = $74.

Let . Use the definition of the derivative to find .

Answer true or false. If , .

Let f(x) = sin x. Estimate by using a graphing utility.

Find , if .

Limits and Continuity

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 2: The Derivative

Find where f(x) = sin 6 5x.

Use the definition of the derivative to calculate f '(x) if f(x) = 2x2 - 2x and find the equation of the tangent line and the normal line to the graph of f at x = 2.

Find the instantaneous rate of change of y = 3x2 with respect to x at x0 = 5.

Find f '(x) if f(x) = x sin x.

Answer true or false. The derivative of the function graphed on the left is graphed on the right.

Let . Find the instantaneous rate of change of y with respect to x at the point x = 5.

Find f '(x) if f(x) = x tan x.

Let f(x) = 3x2. Find the slope of the tangent to the graph of f at a general point x0 using limits and find the slope of the tangent at x0 = 3.

f(x) = sin(6x). f'(x) =

Find equations for the tangent and normal lines to the graph of f(x) = cos(4 - x2) at x = 2.

Find dy/dx if y = 5x8.

Use the definition of the derivative to calculate f '(x) if f(x) = 4x4 + 7 and find the equations of the tangent line and the normal line to the graph of f at x = -4.

Find the equation of the tangent line to at x = 8.

Answer true or false. If x is given in radians, the derivative formula for y = sin x in degrees is .

Answer true or false. If , .

The cost of manufacturing an object is given by C = f(x) dollars. Estimate the cost of making the 310th item if f '(309) = $74.

Let . Use the definition of the derivative to find .

Answer true or false. If , .

Let f(x) = sin x. Estimate by using a graphing utility.

Find , if .

Limits and Continuity

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Find where f(x) = sin ⁶ 5x.

Use the definition of the derivative to calculate f '(x) if f(x) = 2x² - 2x and find the equation of the tangent line and the normal line to the graph of f at x = 2.

Find the instantaneous rate of change of y = 3x² with respect to x at x₀ = 5.

Let f(x) = 3x². Find the slope of the tangent to the graph of f at a general point x₀ using limits and find the slope of the tangent at x₀ = 3.

Find equations for the tangent and normal lines to the graph of f(x) = cos(4 - x²) at x = 2.

Find dy/dx if y = 5x⁸.

Use the definition of the derivative to calculate f '(x) if f(x) = 4x⁴ + 7 and find the equations of the tangent line and the normal line to the graph of f at x = -4.

The cost of manufacturing an object is given by C = f(x) dollars. Estimate the cost of making the 310^th item if f '(309) = $74.