We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

Create An Account

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1491 : Calculus

Find the derivative of the function.

$x^{4}+2x^{2}+3x+6$

Possible Answers:

$4x^{3}+4x+9$

$x^{3}+2x+3$

$4x^{3}+4x+3$

$4x^{4}+4x^{2}+3x$

Correct answer:

$4x^{3}+4x+3$

Explanation:

To find the derivative, use the power rule which states, $(x^n)'=nx^{n-1}$ .

Applying the power rule to each term in the function we get,

$\frac{d}{dx}x^{4}=4x^{3}$

$\frac{d}{dx}2x^{2}=4x$

$\frac{d}{dx}3x=3$ .

Recall that the derivative of a constant is 0.

$\frac{d}{dx}6=0$

Thus, the derivative is:

$4x^{3}+4x+3$

Report an Error

Example Question #272 : How To Find Differential Functions

Find the slope of the tangent line at x=3 .

$x^{2}+7x-3$

Possible Answers:

Correct answer:

Explanation:

Begin by finding the derivative using the power rule which states, $(x^n)'=nx^{n-1}$ .

Applying the power rule to each term in the function we get,

$\frac{d}{dx}x^{2}=2x$

$\frac{d}{dx}7x=7$

Recall that the derivative of a constant is 0.

$\frac{d}{dx}-3=0$

Thus, the derivative is 2x+7 .

Now, substitute 3 for x in order to find the slope of the tangent line at 3.

2(3)+7

Report an Error

Example Question #273 : How To Find Differential Functions

Find the derivative.

$2x^{3}+3x^{2}-9x+4$

Possible Answers:

$x^{3}+x^{2}-x$

$\frac{1}{2}x^{4}+x^{3}-\frac{9}{2}x^{2}+4x$

$6x^{2}+6x-9$

Correct answer:

$6x^{2}+6x-9$

Explanation:

To find the derivative, use the power rule which states, $(x^n)'=nx^{n-1}$ .

Applying the power rule to each term in the function we get,

$\frac{d}{dx}2x^{3}=6x^{2}$

$\frac{d}{dx}3x^{2}$ =6x

$\frac{d}{dx}-9x=-9$ .

Recall that the derivative of a constant is zero.

$\frac{d}{dx}4=0$

Thus, the derivative is:

$6x^{2}+6x-9$

Report an Error

Example Question #271 : How To Find Differential Functions

Find the slope of the tangent line at x=5 .

$\frac{7}{x^{2}}$

Possible Answers:

$-\frac{14}{120}$

$\frac{-14}{125}$

$-\frac{1}{10}$

$-\frac{1}{5}$

Correct answer:

$\frac{-14}{125}$

Explanation:

First, find the derivative by using the quotient rule which states,

$\frac{f(x)}{g(x)}'=\frac{g(x)f'(x)-f(x)g'(x)}{g(x)^2}$ .

In this particular case,

$g(x)=x^2\rightarrow g'(x)=2x$

$f(x)=7\rightarrow f'(x)=0$

Therefore our derivative becomes,

$=\frac{x^2\cdot 0-7\cdot 2x}{(x^2)^2}=\frac{-14x}{x^4}$

$=\frac{-14}{x^3}$

Now, substitute 5 for x.

$\frac{-14}{125}$

Report an Error

Example Question #461 : Functions

Find the derivative.

$x^{3}+2x^{2}+5x-5$

Possible Answers:

$x^{2}+2x+5$

$3x^{2}+4x+5$

$3x^{3}+4x^{2}+5x$

Correct answer:

$3x^{2}+4x+5$

Explanation:

Use the power rule which states, $(x^n)'=nx^{n-1}$ to find the derivative.

Applying the power rule to each term in the function we get,

$\frac{d}{dx}x^{3}=3x^{2}$

$\frac{d}{dx}2x^{2}=4x$

$\frac{d}{dx}5x=5$

Recall that the derivative of a constant equals zero.

$\frac{d}{dx}-5=0$

Thus, the derivative is $3x^{2}+4x+5$ .

Report an Error

Example Question #462 : Functions

Find the derivative of the function.

$2x^{2}(x^{3})$

Possible Answers:

$10x^{4}$

$12x^{3}$

$2x^{5}$

Correct answer:

$10x^{4}$

Explanation:

Use the product rule to find the derivative.

The product rule is,

f(x)g(x)'=f(x)g'(x)+g(x)f'(x) .

Applying this rule to our function we get,

$2x^{2}(3x^{2})+x^{3}(4x)$ .

Simplify.

$\frac{d}{dx}=6x^{4}+4x^{4}$

$\frac{d}{dx}=10x^{4}$

Report an Error

Example Question #1491 : Calculus

Find the slope of the tangent line at x=11 .

$x^{3}(x+3)$

Possible Answers:

1893

1794

1894

6413

Correct answer:

6413

Explanation:

Begin by finding the derivative using the product rule.

The product rule is,

f(x)g(x)'=f(x)g'(x)+g(x)f'(x) .

Applying this rule to our function where

$f(x)=x^3\rightarrow f'(x)=3x^2$

$g(x)=x+3\rightarrow g'(x)=1$

we get,

x^3(1)+(x+3)3x^2

x^3+3x^3+9x^2

4x^3+9x^2

Now, substitute 11 for x.

$4(11)^{3}+9\cdot11^{2}$

=5324+1089

=6413

Report an Error

Example Question #461 : Functions

Find the slope of the tangent line at x=1 .

$(x+3)x^{4}$

Possible Answers:

Correct answer:

Explanation:

Begin by finding the derivative using the product rule.

The product rule is,

f(x)g(x)'=f(x)g'(x)+g(x)f'(x) .

Applying this rule to our function where

$f(x)=(x+3)\rightarrow f'(x)=1$

$g(x)=x^4\rightarrow g'(x)=4x^3$

we get,

$(x+3)4x^3+x^{4}(1)$

$4x^{4}+12x^{3}+x^{4}$

$5x^{4}+12x^{3}$

Now, substitute 1 for x.

Report an Error

Example Question #1493 : Calculus

What is the slope of the tanget line at x=2.5 ?

$2x^{4}-3x^{2}+2$

Possible Answers:

100

110

105

115

Correct answer:

110

Explanation:

First, find the derivative using the power rule which states, $(x^n)'=nx^{n-1}$ .

Applying the power rule to each term in the function we get,

$8x^{3}-6x$

Now, plug in 2.5 for x.

$8(2.5^{3})-6(2.5)$

125-15=110

Report an Error

Example Question #281 : Other Differential Functions

Find the slope of the tangent line at x=1.5 .

$\frac{x^{2}}{4}$

Possible Answers:

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{1}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

First, find the derivative using the quotient rule which states,

$\frac{f(x)}{g(x)}'=\frac{g(x)f'(x)-f(x)g'(x)}{g(x)^2}$ .

In this particular case,

$f(x)=x^2\rightarrow f'(x)=2x$

$g(x)=4\rightarrow g'(x)=0$ .

Therefore the derivative becomes,

$\frac{4(2x)-x^2(0)}{4^2}=\frac{4(2x)}{16}$

$=\frac{8x}{16}=\frac{x}{2}$

Now, substitute 1.5 for x.

$\frac{1.5}{2}=\frac{3}{4}$

Report an Error

View Calculus Tutors

Isabella
Certified Tutor

Iowa State University, Bachelor of Science, Mathematics.

View Calculus Tutors

Nadim
Certified Tutor

University of Rochester, Bachelor of Science, Computational Biology. New York Institute of Technology, Doctor of Medicine, Os...

View Calculus Tutors

Nathan
Certified Tutor

California Polytechnic State University, San Luis Obispo, Bachelor, Electrical Engineering.

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Atlanta, English Tutors in San Francisco-Bay Area, Biology Tutors in San Diego, GRE Tutors in Denver, ACT Tutors in Denver, Calculus Tutors in San Diego, Computer Science Tutors in Seattle, English Tutors in New York City, English Tutors in Phoenix, Biology Tutors in Chicago

Popular Courses & Classes

SAT Courses & Classes in Los Angeles, SAT Courses & Classes in Houston, MCAT Courses & Classes in Phoenix, Spanish Courses & Classes in Phoenix, MCAT Courses & Classes in Washington DC, SAT Courses & Classes in Denver, Spanish Courses & Classes in Seattle, MCAT Courses & Classes in Denver, Spanish Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Boston

Popular Test Prep

LSAT Test Prep in Phoenix, LSAT Test Prep in Chicago, GRE Test Prep in Chicago, MCAT Test Prep in Seattle, ISEE Test Prep in Houston, ISEE Test Prep in Phoenix, SAT Test Prep in San Diego, MCAT Test Prep in Philadelphia, GMAT Test Prep in Los Angeles, ISEE Test Prep in Chicago

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #1491 : Calculus

Example Question #272 : How To Find Differential Functions

Example Question #273 : How To Find Differential Functions

Example Question #271 : How To Find Differential Functions

Example Question #461 : Functions

Example Question #462 : Functions

Example Question #1491 : Calculus

Example Question #461 : Functions

Example Question #1493 : Calculus

Example Question #281 : Other Differential Functions

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: