Call Now to Set Up Tutoring:

(888) 888-0446

AP Calculus AB : Understanding the derivative of a sum, product, or quotient

Study concepts, example questions & explanations for AP Calculus AB

CREATE AN ACCOUNT Create Tests & Flashcards

Home Embed

All AP Calculus AB Resources

3 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Understanding The Derivative Of A Sum, Product, Or Quotient

Find the derivative of the following function:

$f(x) = x^3 + \frac{1}{x}$

Possible Answers:

$f'(x) = 3x^2-\frac{1}{x}$

f'(x) = 3x^2+x

f'(x) = 3x^2

$f'(x) = 3x^2+\frac{1}{x^2}$

$f'(x) = 3x^2-\frac{1}{x^2}$

Correct answer:

$f'(x) = 3x^2-\frac{1}{x^2}$

Explanation:

Since this function is a polynomial, we take the derivative of each term separately.

From the power rule, the derivative of

x^3

is simply

3x^2

We can rewrite $\frac{1}{x}$ as

$x^{-1}$

and using the power rule again, we get a derivative of

$-x^{-2}$ or $-\frac{1}{x^2}$

So the answer is

$f'(x) = 3x^2-\frac{1}{x^2}$

Report an Error

Example Question #1 : Understanding The Derivative Of A Sum, Product, Or Quotient

What is $\frac{\mathrm{d} }{\mathrm{d} x}f(x)*g(x)\mathrm{d x} ?$

Possible Answers:

f(x)g'(x)+f'(x)g(x)

f(x)g'(x)-f'(x)g(x)

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

f(x)g(x)+f'(x)g'(x)

f(x)*f'(x)+g(x)*g'(x)

Correct answer:

f(x)g'(x)+f'(x)g(x)

Explanation:

The chain rule is "first times the derivative of the second plus second times derivative of the first".

In this case, that means $\frac{\mathrm{d} }{\mathrm{d} x}f(x)*g(x)\mathrm{d x} =f(x)g'(x)+f'(x)g(x)$ .

Report an Error

Example Question #3 : Understanding The Derivative Of A Sum, Product, Or Quotient

Which of the following best represents $\frac{\mathrm{d} }{\mathrm{d} x}\frac{f(x)}{g(x)}$ ?

Possible Answers:

$\frac{f'(x)}{g'(x)}$

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

f'(x)g(x)+g'(x)f(x)

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

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

Correct answer:

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

Explanation:

The question is just asking for the Quotient Rule formula.

Recall the Quotient Rule is the bottom function times the derivative of the top minus the top function times the derivative of the bottom all divided by the bottom function squared.

Given,

$\frac{\mathrm{d} }{\mathrm{d} x}\frac{f(x)}{g(x)}$

the bottom function is g(x) and the top function is f(x) . This makes the bottom derivative g'(x) and the top derivative f'(x) .

Substituting these into the Quotient Rule formula resulting in the following.

$\frac{\mathrm{d} }{\mathrm{d} x}\frac{f(x)}{g(x)}=\frac{g(x)\cdot f'(x)-f(x)\cdot g'(x)}{(g(x))^2}$

Report an Error

View AP Calculus AB Tutors

Alan
Certified Tutor

Stanford University, Bachelor of Science, Electrical Engineering. University of North Carolina at Chapel Hill, Masters in Bus...

View AP Calculus AB Tutors

Aris
Certified Tutor

Connecticut College, Bachelor of Science, Mathematics.

View AP Calculus AB Tutors

Daniel
Certified Tutor

University of Oregon, Bachelor of Science, Physics.

All AP Calculus AB Resources

3 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in New York City, Math Tutors in Houston, GRE Tutors in Philadelphia, GMAT Tutors in Houston, Chemistry Tutors in Atlanta, Statistics Tutors in Philadelphia, English Tutors in Atlanta, GRE Tutors in New York City, MCAT Tutors in San Francisco-Bay Area, Computer Science Tutors in New York City

Popular Courses & Classes

MCAT Courses & Classes in Los Angeles, SAT Courses & Classes in Denver, Spanish Courses & Classes in Philadelphia, SSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Miami, SSAT Courses & Classes in Chicago, GRE Courses & Classes in Los Angeles, ACT Courses & Classes in Boston, MCAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Boston

Popular Test Prep

MCAT Test Prep in Houston, LSAT Test Prep in Seattle, SSAT Test Prep in Phoenix, SSAT Test Prep in Boston, ACT Test Prep in Denver, ACT Test Prep in Boston, SSAT Test Prep in Atlanta, LSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Houston, GRE Test Prep in Atlanta

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

AP Calculus AB : Understanding the derivative of a sum, product, or quotient

Study concepts, example questions & explanations for AP Calculus AB

All AP Calculus AB Resources

Example Questions

Example Question #1 : Understanding The Derivative Of A Sum, Product, Or Quotient

Example Question #1 : Understanding The Derivative Of A Sum, Product, Or Quotient

Example Question #3 : Understanding The Derivative Of A Sum, Product, Or Quotient

All AP Calculus AB Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

FIND THE BEST TUTORS

Email address:
Your name:

Email address:
Your name:
Feedback: