We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Chain Rule

Study concepts, example questions & explanations for GRE Subject Test: Math

Create An Account

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Derivatives & Integrals

Compute the derivative:

y=cos(sin(2x))

Possible Answers:

-2cos^2(2x)

-2sec(2x)tan(2x)

-2cos(2x)sin(sin(2x))

-2cos(2x)sin^2(2x)

-2sin^2(2x)

Correct answer:

-2cos(2x)sin(sin(2x))

Explanation:

This question requires application of multiple chain rules. There are 2 inner functions in y=cos(sin(2x)) , which are sin(2x) and .

The brackets are to identify the functions within the function where the chain rule must be applied.

Solve the derivative.

$\frac{dy}{dx}= -sin([sin(2x)]) \cdot (cos[2x]))\cdot 2=-2cos(2x)sin(sin(2x))$

The sine of sine of an angle cannot be combined to be sine squared.

Therefore, the answer is:

-2cos(2x)sin(sin(2x))

Report an Error

Example Question #12 : Derivatives & Integrals

Find the derivative of the following function:

$h(x)=(3x^3-4x)^{33}$

Possible Answers:

$h'(x)=(9x^2-4)(3x^2-4x)^{32}$

$h'(x)=(297x^2+132)(3x^2-4x)^{33}$

$h'(x)=(297x^2-132)(3x^2-4x)^{33}$

$h'(x)=(297x^2)(3x^2-4x)^{32}$

$h'(x)=(297x^2-132)(3x^2-4x)^{32}$

Correct answer:

$h'(x)=(297x^2-132)(3x^2-4x)^{32}$

Explanation:

Recall chain rule for this problem

(f(g(x)))'=f'(g(x))g'(x)

So if we are given the following,

$h(x)=(3x^3-4x)^{33}$

We can think of it like this

f(x)=3x^3-4x

f'(x)=9x^2-4

$g(x)=x^{33}$

$g'(x)=33x^{32}$

$(f(g(x)))'=(9x^2-4)(33)(3x^2-4x)^{32}$

Clean it up a bit to get:

$(f(g(x)))'=(297x^2-132)(3x^2-4x)^{32}$

Report an Error

Example Question #1 : Chain Rule

What is the derivative of 3x^2*8y^3

Possible Answers:

3x^2*24y^2+8y^3*6x

6x*24y

3x^2*24y^2

8y^3*6x

3x*8y^2

Correct answer:

3x^2*24y^2+8y^3*6x

Explanation:

Chain Rule: Given: f(x)*g(y)

$\frac{\mathrm{dy} }{\mathrm{d} x}=f(x)g'(y)+g(y)f'(x)$

For this problem

f(x)=3x^2

$f'(x)=\frac{\mathrm{d} }{\mathrm{d} x}3x^2=3(2)x^{2-1}=6x$

g(y)=8y^3

$g'(y)=\frac{\mathrm{d} }{\mathrm{d} x}8y^3=8(3)y^{3-1}=24y^2$

Plug the values into the Chain Rule formula and simplify:

$\frac{\mathrm{dy} }{\mathrm{d} x}(3x^2*8y^3)=3x^2*24y^2+8y^3*6x$

Report an Error

View Tutors

Samuel
Certified Tutor

York University, Bachelor, Physics. York University, Master's/Graduate, Mathematics and Statistics.

View Tutors

Mohammed
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Electrical Engineering. University of Maryland-College Park, Master...

View Tutors

Sumit
Certified Tutor

Calcutta University, Bachelor of Science, Mathematics. Indian Statistical Institute, Master of Science, Mathematics.

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in San Diego, English Tutors in Phoenix, GRE Tutors in New York City, Calculus Tutors in San Francisco-Bay Area, French Tutors in Denver, English Tutors in Washington DC, Physics Tutors in San Francisco-Bay Area, Physics Tutors in Chicago, Math Tutors in Philadelphia, English Tutors in San Francisco-Bay Area

Popular Courses & Classes

SAT Courses & Classes in Boston, SSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Miami, GMAT Courses & Classes in Washington DC, Spanish Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Atlanta, GRE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Seattle, GMAT Courses & Classes in Atlanta

Popular Test Prep

GRE Test Prep in New York City, MCAT Test Prep in Los Angeles, GMAT Test Prep in Dallas Fort Worth, SAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Washington DC, ISEE Test Prep in Atlanta, MCAT Test Prep in Philadelphia, GMAT Test Prep in Atlanta, SAT Test Prep in Philadelphia, SSAT Test Prep in Philadelphia

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

GRE Subject Test: Math : Chain Rule

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #11 : Derivatives & Integrals

Example Question #12 : Derivatives & Integrals

Example Question #1 : Chain Rule

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: