Skip to main content

close

Start your trial now! First week only $4.99!

arrow_forward

Literature guides

Concept explainers

Writing guide

Popular textbooks

Popular high school textbooks

Popular Q&A

Business

Accounting

Business Law

Economics

Finance

Leadership

Management

Marketing

Operations Management

Engineering

AI and Machine Learning

Bioengineering

Chemical Engineering

Civil Engineering

Computer Engineering

Computer Science

Cybersecurity

Data Structures and Algorithms

Electrical Engineering

Mechanical Engineering

Language

Spanish

Math

Advanced Math

Algebra

Calculus

Geometry

Probability

Statistics

Trigonometry

Science

Advanced Physics

Anatomy and Physiology

Biochemistry

Biology

Chemistry

Earth Science

Health & Nutrition

Health Science

Nursing

Physics

Social Science

Anthropology

Geography

History

Political Science

Psychology

Sociology

learn

write

expand_more

plus

study resources

expand_more

Log In

Sign Up

expand_more

menu

SEARCH

Homework help starts here!

ASK AN EXPERT

ASK

Math

Calculus

The derivative of the function y = 7x² + 12 – is: – 15 a) y’ = 14x + x2 15 %3D b) y’ = 14x + %3D c) y’ = 14x + 12 +5 %3D

The derivative of the function y = 7x² + 12 – is: – 15 a) y’ = 14x + x2 15 %3D b) y’ = 14x + %3D c) y’ = 14x + 12 +5 %3D

BUY

Calculus: Early Transcendentals

8th Edition

ISBN:

9781285741550

Author: James Stewart

Publisher:

Cengage Learning

expand_less

1 Functions And Models

2 Limits And Derivatives

3 Differentiation Rules

4 Applications Of Differentiation

5 Integrals

6 Applications Of Integration

7 Techniques Of Integration

8 Further Applications Of Integration

9 Differential Equations

10 Parametric Equations And Polar Coordinates

11 Infinite Sequences And Series

12 Vectors And The Geometry Of Space

13 Vector Functions

14 Partial Derivatives

15 Multiple Integrals

16 Vector Calculus

17 Second-order Differential Equations

expand_more

1.1 Four Ways To Represent A Function

1.2 Mathematical Models: A Catalog Of Essential Functions

1.3 New Functions From Old Functions

1.4 Exponential Functions

1.5 Inverse Functions And Logarithms

Chapter Questions

expand_more

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How…

Problem 2RCC: Discuss four ways of representing a function. Illustrate your discussion with examples.

Problem 3RCC: (a) What is an even function? How can you tell if a function is even by looking at its graph? Give…

Problem 4RCC: What is an increasing function?

Problem 5RCC: What is a mathematical model?

Problem 6RCC: Give an example of each type of function. (a) Linear function (b) Power function (c) Exponential…

Problem 7RCC: Sketch by hand, on the same axes, the graphs of the following functions. (a) f(x) = x (b) g(x) = x2…

Problem 8RCC: Draw, by hand, a rough sketch of the graph of each function. (a) y = sin x (b) y = tan x (c) y = ex…

Problem 9RCC: Suppose that f has domain A and g has domain B. (a) What is the domain of f + g? (b) What is the…

Problem 10RCC: How is the composite function f g defined? What is its domain?

Problem 11RCC: Suppose the graph of f is given. Write an equation for each of the graphs that are obtained from the…

Problem 12RCC: (a) What is a one-to-one function? How can you tell if a function is one-to-one by looking at its…

Problem 13RCC: (a) How is the inverse sine function f(x) = sin1 x defined? What are its domain and range? (b) How…

Problem 1RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 2RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 3RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 4RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 5RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 6RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 7RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 8RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 9RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 10RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 11RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 12RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 13RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 14RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,…

Problem 1RE: Let f be the function whose graph is given. (a) Estimate the value of f(2). (b) Estimate the values…

Problem 2RE: The graph of g is given. (a) State the value of g(2). (b) Why is g one-to-one? (c) Estimate the…

Problem 3RE: lf f(x) = x2 2x + 3, evaluate the difference quotient f(a+h)f(a)h

Problem 4RE: Sketch a rough graph or the yield of a crop as a function of the amount of fertilizer used.

Problem 5RE: Find the domain and range of the function. Write your answer in interval notation. 5. f(x) = 2/(3x …

Problem 6RE: Find the domain and range of the function. Write your answer in interval notation. 6. g(x)=16×4

Problem 7RE

Problem 8RE: Find the domain and range of the function. Write your answer in interval notation. 8. F(t) = 3 + cos…

Problem 9RE

Problem 10RE: The graph of .f is given. Draw the graphs of the following functions. (a) y = f(x 8) (b) y = f(x)…

Problem 11RE

Problem 12RE: Use transformations to sketch the graph of the function. y=2x

Problem 13RE

Problem 14RE: Use transformations to sketch the graph of the function. y = In(x + 1)

Problem 15RE: Use transformations to sketch the graph of the function. f(x) = cos 2x

Problem 16RE: Use transformations to sketch the graph of the function. f(x)={xifx0ex1ifx0

Problem 17RE: Determine whether f is even, odd, or neither even nor odd. (a) f(x)=2x53x2+2. (h) f(x) = x3 x7 (c)…

Problem 18RE: Find an expression for the function whose graph consists of the line segment from point (2, 2) to…

Problem 19RE: If f(x) = In x and g(x) = x2 9. find the functions (a) fg (b) gf (c) ff (d) gg, and their domains.

Problem 20RE: Express the function F(x)=1/x+x as a composition of three functions.

Problem 22RE: A small-appliance manufacturer finds that it costs 9000 to produce 1000 toaster ovens a week and…

Problem 23RE: If f(x) = 2x + In x, find f1(2).

Problem 24RE: Find the inverse function of f(x)=x+12x+1.

Problem 25RE: Find the exact value of each expression. 64. (a) tan13 (b) arctan (1) 25. Find the exact value of…

Problem 26RE

Problem 27RE: The half-life of palladium-100, 100Pd, is four days. (So half of any given quantity of 100Pd will…

Problem 28RE: The population of a certain species in a limited environment with initial population 100 and…

Problem 1P: One of the legs of a right triangle has length 4 cm. Express the length of the altitude…

Problem 2P: The altitude perpendicular to the hypotenuse of a right triangle is 12 cm. Express the length of the…

Problem 3P: Solve the equation |2x 1| |x + 5| = 3.

Problem 4P: Solve the inequality |x 1| |x 3| 5.

Problem 5P

Problem 6P: Sketch the graph of the function g(x) = |x2 1 | |x2 4|.

Problem 7P

Problem 8P

Problem 9P: The notation max{a, b, } means the largest of the numbers a, b. Sketch the graph of each function….

Problem 10P: Sketch the region in the plane defined by each of the following equations or inequalities. (a)…

Problem 11P: Evaluate (log2 3)(log3 4)(log4 5)(log31 32).

Problem 12P: (a) Show that the function f(x)=ln(x+x2+1) is an odd function. (b) Find the inverse function of f.

Problem 13P: Solve the inequality ln(x2 2x 2) 0.

Problem 14P: Use indirect reasoning to prove that log2 5 is an irrational number.

Problem 15P: A driver sets out on a journey. For the first half of the distance she drives at the leisurely pace…

Problem 16P: Is it true that f(g+h)=fg+fh?

Problem 17P: Prove that if n is a positive integer, then 7n 1 is divisible by 6.

Problem 18P: Prove that 1 + 3 + 5 + + (2n l ) = n2.

Problem 19P: If fo(x) = x2 and fn+1(x) = fo(fn(x)) for n = 0, 1, 2,, find a formula for fn(x).

Problem 20P: (a) If fo(x)=12x and fn+1=fofnforn=0,1,2,, find an expression for fn(x) and use mathematical…

format_list_bulleted

See similar textbooks

Related questions

Q: Find the derivative using the theorems on derivatives. dx x2-2 1 y = 2.y = (x² – 1)³(x² + 3)² x3+4x…

A: Given functions to be differentiate are 1. y=x2-2×3+4x 3. y=x2-2x we will make use…

Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx point (1,-1,1) in the direction 3i+4k x at…

A:

Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t; dy dx

A:

Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec = sec-1 27) y = -sin-1 (5×2 + 2) 28)…

A:

Q: Determine the derivative of the following functions. 1. у 3 (8ӕ — 1) sinh(8a — 1) 2. y = (5)…

A:

Q: Find the derivative of y with respect to the appropriate variable 53. у %3D sec (2s + 1) 55. y =…

A:

Q: he first derivative of y = 3x ++ 2V – a is %3D 3 10 y’ 5 5z 5 3z 3 3 O y’ 10 %3D 2V14 3 O y’ 3. 10…

A: To find the derivative of: y=3×15-23x+35+2×34-5×23⇒y=3×15-23x+35+2×34-5x-23…(1) Note that:…

Q: yニア×tanx

A: To find the derivative of y.

Q: Find the Indicated Derivative for Higher-Order 1. y = 10×5 – 21×4 + 13×3 – 6×2 + 5x – 1000 ; y(6)…

A:

Q: The 2nd derivative of the given functions is 3 ponts y = 3 cos (4x- 5) None of the above -48 cos…

A:

Q: y = x* + 2 sin(x) + xº + 24*.

A:

Q: Obtain the derivative of the function y 4y sen (3x) – 7x In(2x + y) = e* – ey + 4tg(y)

A:

Q: Use forward difference approximation to estimate the first derivative of the following equation.…

A: Given that, fx=-0.15×3-0.2×2-0.5x+2.25h=0.5We need to find the first derivative of the function at…

Q: Find the derivative of the function. y=x5 7 3×7 O y’=- 2×3.7 O Y’33 O Y’=. 2×3.7 O Y’=. 3×7 + 5×4…

A: Given, y=x5x3+7

Q: Find the derivative of y given that coth-1 (21x³) y = 63×2 A 1–441×6 63×2 B 1–441×6 63×2 1+441×6…

A: Given y=coth-121×3

Q: Calculate up to 2nd derivative the equation g(x) = -8sin (*+1) %3D

A:

Q: Find the derivative of y with respect to x. y = cos1 (5×2 + 4) 10x + (5×2 + 4)2 -10x Vi- (5×2 + 4)?…

A: The given function is y= cos-1(5×2+4) We have to find the derivative of this function w.r.t. x

Q: The third derivative of y = sin is 1 -sin b) y” = –cos 1 а) у 8. 2 2 c) y” =-8sin d) y” = -8 cos

A:

Q: Find the derivative of y with respect to x. -1 2х + 3 26) y = sec” 27) y = -sin-1 (5×2 + 2) 28) y =…

A:

Q: what is the derivative of this question with solution y= csc (4x² ) Arccsc (4x² )

A:

Q: Determine the derivative of y=tan(cos-(4x)). -1 A y’=. 4XV1- 16×2 None of the given choices -1 y’s…

A:

Q: Find the derivative. 5х + 1 In 5x – 1 dx 5x +1 %3D dx 5x -1)

A:

Q: The derivative of y = 3cos(8x+6) is: 1. y’ = 24 sin (8x+6) 2. y’ = -24 sin (8x+6) 3. y’ = -24 cos…

A:

Q: The derivative of the function y = etan(4x) is: a) y’ = tan (4x)etan(4x) b) y’ = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: Find the second derivative of y = (4 – 2x)2 + 2sinx. dy Directly type your answer WITHOUT y’ or dx…

A:

Q: Find the Indicated Derivative dy 1. y = x5 – 3x* + 2×3 – 2×2 + 7x – 1, dx dy 2. y =x2+x-3 + 3, dx…

A: Given:- y = x5 -3×4 +2×3 -2×2 +7x-1 y =0.5x-2 + (2x-3/3) +3 To find:- dy/dx

Q: What is the derivative of y x2 e+ 3x -2 ? %3D O y = (6x³ + 3x? +2) ez?+2z – 2 %3D O y = (6x + 3)…

A: Topic = Derivataive

Q: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y)=xy, What is…

A: To find the derivative of y with respect to x

Q: derivative of g(x)= intergral from 1 to root x, (z^2)/z^4+1

A: ddx∫1xz2z4+1dz

Q: Find the derivative of f(z) = 3+ 2x² – 2y² + i4xy .

A: We find out the derivative of given function .we differentiate both sides with respect to z and take…

Q: ) Find the derivative of y = [7 cos5(5x – 8)(cos³V2x – 1)] %3D

A:

Q: Find the function that passes through the point (1,2) and whose derivative is dy/dx = (2/x^3) – 4

A: Topic:- application of integration

Q: Find the derivative of f (x ) =V sech( In (8x + 1)) – sech(In(8x + 1)) tanh( In(8x + 1)) A 2/ sech(…

A:

Q: What is the derivative of y = tan-1(x2 + 1)? dy dr 2 1+( z²+1)² dy dr /1+(z²+1)² dy O dr V1+(2+1 )°…

A: To find derivative of y=tan-1×2+1

Q: The derivative of sec(e) is tanx O 1) tan(e*”) sec{e*™) O 2) tan(e**) sec(e*)x e** 3) tan(e)…

A: topic – derivative of a function

Q: Find the partial derivative. 4 = (x² + 6x – 3y)* – dz

A:

Q: With respect to u, what is the derivative of: * 12 בV 2 2 dx Option1 Option3 -‘/2 -15

A: Answer is mentioned below –

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 3. y = V(4x + 3)³

A: To find the third derivative of y=(4x+3)34⇒y=(4x+3)34 The general rule of differentiation is…

Q: Зx+1 5. f(x) %3D 3×2+2

A: f(x)=3x+13×2+2Differentiate…

Q: Use Quotient Rule to find the derivative. x² + x – 2 3x +1: dy 2x+1 A. dx 3x + 1 dy B.…

A:

Q: Find the linear approximation of the function f (x,y) = ln (x – 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Determine the derivative -d/dv y = 2x³ + 5x – 6 y 1 x² 3x 6x³ + x² − 10x − 3 –

A:

Q: Find the derivative of 5e* 1. y = e 6x 3. y = 2x+3x 2. y = e* + e3x 4. y = (e* + ex)1/2

A: Quotient Rule of differentiation : ddxuv=v.dudx-dvdx.uv2 deaxdx=aeax dxndx=n.xn-1

Q: What is the second derivative of y = sec “(3 x) ?

A: For the question 1, none of the options match. If the question had asked for first derivative of y…

Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 dy dx dy = -2(x + 1)(x2 + 1)-4(2×2 + 3x – 1) A) B) Y…

A: We can find the correct answer as below.

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: What is the derivative of y = (sin (3x?)2? dy dr 12z sin’ (3교2) VI-974 dy dr 12z sin (3z²) VI-9z4 dy…

A:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

A:

Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY – sin x4 dx C) dy – -4×4…

A:

Q: . The derivative of y = 3VX4 – cosx is – D. x*/3 + cosx A. x/3 + sinx В. 4х /з + sinx C. 4x*/3 +…

A: y=3×43-cosx⇒y=3×43-cosxThen dydx=(3×43×x43-1)-(-sinx) =4×13+sinx

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Question

Transcribed Image Text:

Question 5* The derivative of the function y = 7x² + 12 – 5. is: a) y’ = 14x + 15 x² 15 b) y’ = 14x + c) y’ = 14x + 12 + 15 a Question 6* W

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

See solution

Check out a sample Q&A here

Knowledge Booster

Learn more about

Application of Differentiation

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

arrow_back_ios

arrow_forward_ios

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas’ Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas’ Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS