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

The answer of Find f '(x) where ....

Find if y = $\alpha$ 11 . (Alpha is a constant.)

The answer of Find if y = $\alpha$...

g(x) = x4f(x). Find g'(4), given that f(4) = 3 and f '(4) = 6.

A) 1,792 B) 1,024 C) 2,304 D) 4,608 E) 1,536 A) 1,792 B) 1,024 C) 2,304 D) 4,608 E) 1,536

Exam 2: The Derivative

A rock is dropped from a height of 400 feet and falls toward the earth in a straight line. In t seconds, the rock drops a distance of s = 16t² feet. What is the average velocity of the rock while it is falling? Use limits to find the instantaneous velocity of the rock when it hits the ground.

(Essay)

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Question 41

Let . Find the average rate of change of y with respect to x over the interval [3, 5].

(Essay)

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Question 42

If ,

(Multiple Choice)

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Question 43

Find f '(x) where .

(Essay)

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Question 44

Find the average rate of change of y with respect to x for over the interval [1, 8].

(Multiple Choice)

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Question 45

Answer true or false. If f, g, and h are differentiable functions, and h $\neq$ 0 anywhere on its domain, then $Answer true or false. If f, g, and h are differentiable functions, and h \neq 0 anywhere on its domain, then .$ .

(True/False)

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Question 46

If y = x⁸ + 4x³, find .

(Essay)

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Question 47

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

(Multiple Choice)

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Question 48

Answer true or false. A graphing utility will show that is differentiable at x = -1.

(True/False)

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Question 49

Find the instantaneous rate of change of f(x) = -2x⁴ - 11 at x₀ = 2.

(Short Answer)

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Question 50

A rock at an elevation angle of $\theta$ is falling in a straight line. If at a given instant it has an angle of elevation of $\theta$ = $A rock at an elevation angle of \theta is falling in a straight line. If at a given instant it has an angle of elevation of \theta = and is a horizontal distance s from an observer, find the rate at which the rock is falling with respect to \theta .$ and is a horizontal distance s from an observer, find the rate at which the rock is falling with respect to $\theta$ .

(Multiple Choice)

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Question 51

Find $Find if y = \alpha <sup>11</sup> . (Alpha is a constant.)$ if y = $\alpha$ ¹¹ . (Alpha is a constant.)

(Short Answer)

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Question 52

g(x) = x⁴f(x). Find g'(4), given that f(4) = 3 and f '(4) = 6.

(Multiple Choice)

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Question 53

Find if y = .

(Essay)

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Question 54

y = x³ cos(3x). Find dy/dx.

(Short Answer)

4.8/5

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Question 55

Find y'''(3) if y = x⁵.

(Short Answer)

4.9/5

(71)

Question 56

The surface area of a sphere is given by S = 4 $\pi$ r² where r is the radius of the sphere. Use the method of Section 3.2 to find the instantaneous rate of change of S with respect to r when r = 2.

(Essay)

4.7/5

(82)

Question 57

Find (f $\circ$ g)'(3) if f '(3) = 5, g(3) = 3 and g '(3) = 2.

(Essay)

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Question 58

Use a graphing utility to show that does not have a derivative at x = 0.

(Essay)

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Question 59

Sketch the graph of the derivative of the function whose graph is shown.

(Essay)

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Question 60

Showing 41 - 60 of 198

A rock is dropped from a height of 400 feet and falls toward the earth in a straight line. In t seconds, the rock drops a distance of s = 16t² feet. What is the average velocity of the rock while it is falling? Use limits to find the instantaneous velocity of the rock when it hits the ground.

Let . Find the average rate of change of y with respect to x over the interval [3, 5].

If ,

Find f '(x) where .

Find the average rate of change of y with respect to x for over the interval [1, 8].

Answer true or false. If f, g, and h are differentiable functions, and h $\neq$ 0 anywhere on its domain, then $Answer true or false. If f, g, and h are differentiable functions, and h \neq 0 anywhere on its domain, then .$ .

If y = x⁸ + 4x³, find .

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

Answer true or false. A graphing utility will show that is differentiable at x = -1.

Find the instantaneous rate of change of f(x) = -2x⁴ - 11 at x₀ = 2.

Find $Find if y = \alpha <sup>11</sup> . (Alpha is a constant.)$ if y = $\alpha$ ¹¹ . (Alpha is a constant.)

g(x) = x⁴f(x). Find g'(4), given that f(4) = 3 and f '(4) = 6.

Find if y = .

y = x³ cos(3x). Find dy/dx.

Find y'''(3) if y = x⁵.

The surface area of a sphere is given by S = 4 $\pi$ r² where r is the radius of the sphere. Use the method of Section 3.2 to find the instantaneous rate of change of S with respect to r when r = 2.

Find (f $\circ$ g)'(3) if f '(3) = 5, g(3) = 3 and g '(3) = 2.

Use a graphing utility to show that does not have a derivative at x = 0.

Sketch the graph of the derivative of the function whose graph is shown.

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

A rock is dropped from a height of 400 feet and falls toward the earth in a straight line. In t seconds, the rock drops a distance of s = 16t2 feet. What is the average velocity of the rock while it is falling? Use limits to find the instantaneous velocity of the rock when it hits the ground.

Let . Find the average rate of change of y with respect to x over the interval [3, 5].

If ,

Find f '(x) where .

Find the average rate of change of y with respect to x for over the interval [1, 8].

Answer true or false. If f, g, and h are differentiable functions, and h ≠\neq= 0 anywhere on its domain, then .

If y = x8 + 4x3, find .

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

Answer true or false. A graphing utility will show that is differentiable at x = -1.

Find the instantaneous rate of change of f(x) = -2x4 - 11 at x0 = 2.

A rock at an elevation angle of θ\thetaθ is falling in a straight line. If at a given instant it has an angle of elevation of θ\thetaθ = and is a horizontal distance s from an observer, find the rate at which the rock is falling with respect to θ\thetaθ .

Find if y = α\alphaα 11 . (Alpha is a constant.)

g(x) = x4f(x). Find g'(4), given that f(4) = 3 and f '(4) = 6.

Find if y = .

y = x3 cos(3x). Find dy/dx.

Find y'''(3) if y = x5.

The surface area of a sphere is given by S = 4 π\piπ r2 where r is the radius of the sphere. Use the method of Section 3.2 to find the instantaneous rate of change of S with respect to r when r = 2.

Find (f ∘\circ∘ g)'(3) if f '(3) = 5, g(3) = 3 and g '(3) = 2.

Use a graphing utility to show that does not have a derivative at x = 0.

Sketch the graph of the derivative of the function whose graph is shown.

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

A rock is dropped from a height of 400 feet and falls toward the earth in a straight line. In t seconds, the rock drops a distance of s = 16t² feet. What is the average velocity of the rock while it is falling? Use limits to find the instantaneous velocity of the rock when it hits the ground.

Answer true or false. If f, g, and h are differentiable functions, and h $\neq$ 0 anywhere on its domain, then $Answer true or false. If f, g, and h are differentiable functions, and h \neq 0 anywhere on its domain, then .$ .

If y = x⁸ + 4x³, find .

Find the instantaneous rate of change of f(x) = -2x⁴ - 11 at x₀ = 2.

Find $Find if y = \alpha <sup>11</sup> . (Alpha is a constant.)$ if y = $\alpha$ ¹¹ . (Alpha is a constant.)

g(x) = x⁴f(x). Find g'(4), given that f(4) = 3 and f '(4) = 6.

y = x³ cos(3x). Find dy/dx.

Find y'''(3) if y = x⁵.

The surface area of a sphere is given by S = 4 $\pi$ r² where r is the radius of the sphere. Use the method of Section 3.2 to find the instantaneous rate of change of S with respect to r when r = 2.

Find (f $\circ$ g)'(3) if f '(3) = 5, g(3) = 3 and g '(3) = 2.