Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Implicit Differentiation

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 #1 : Implicit Differentiation

Differentiate the following with respect to .

$3y^2+12x-6\cos x=-4y^3$

Possible Answers:

$\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{-\sin x +2}{y +2 y^2}$

$\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{-(\cos x +2)}{y +2 y^2}$

$\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{-(\sin x +2)}{y +2 y^2}$

$\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{\sin x -2}{y +2 y^2}$

Correct answer:

$\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{-(\sin x +2)}{y +2 y^2}$

Explanation:

The first step is to differentiate both sides with respect to :

$3y^2 \ \frac{\mathrm{d} }{\mathrm{d} x}+12x \ \frac{\mathrm{d} }{\mathrm{d} x}-6\cos x \ \frac{\mathrm{d} }{\mathrm{d} x}=-4y^3\frac{\mathrm{d} }{\mathrm{d} x}$

Note: Those that are functions of can be differentiated with respect to , just remember to mulitply it by $\frac{\mathrm{d} y}{\mathrm{d} x}$

$6y \ \frac{\mathrm{d}y }{\mathrm{d} x}+12+6\sin x =-12y^2\frac{\mathrm{d} y}{\mathrm{d} x}$

Now we can solve for $\frac{\mathrm{d} y}{\mathrm{d} x}$ :

$6y \ \frac{\mathrm{d}y }{\mathrm{d} x}+12 y^2\frac{\mathrm{d} y}{\mathrm{d} x}=-6\sin x -12$

$(6y +12 y^2) \ \frac{\mathrm{d} y}{\mathrm{d} x}=-6(\sin x +2)$

$\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{-6(\sin x +2)}{6(y +2 y^2)}$

$\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{-(\sin x +2)}{y +2 y^2}$

Report an Error

Example Question #2 : Implicit Differentiation

Find

$\frac{\mathrm{d} y}{\mathrm{d} x}$ for x^2+2y^3=8 .

Possible Answers:

$\frac{\mathrm{d}y }{\mathrm{d} x}=\frac{x^2}{2y^2}$

$\frac{\mathrm{d}y }{\mathrm{d} x}=\frac{x}{3y^2}$

$\frac{\mathrm{d}y }{\mathrm{d} x}=\frac{-x}{3y^2}$

$\frac{\mathrm{d}y }{\mathrm{d} x}=\frac{-x}{3y}$

Correct answer:

$\frac{\mathrm{d}y }{\mathrm{d} x}=\frac{-x}{3y^2}$

Explanation:

Our first step would be to differentiate both sides with respect to :

$x^2 \frac{\mathrm{d} }{\mathrm{d} x}+2y^3 \frac{\mathrm{d} }{\mathrm{d} x}=8 \frac{\mathrm{d} }{\mathrm{d} x}$

The functions of can be differentiated with respect to , just remember to multiply by $\frac{\mathrm{d} y}{\mathrm{d} x}$ .

$2x + 6y^2 \frac{\mathrm{d}y }{\mathrm{d} x}=0$

$\frac{\mathrm{d}y }{\mathrm{d} x}=\frac{-2x}{6y^2}$

$\frac{\mathrm{d}y }{\mathrm{d} x}=\frac{-x}{3y^2}$

Report an Error

Example Question #3 : Implicit Differentiation

Differentiate the following to solve for $\frac{\mathrm{d} y}{\mathrm{d} x}$ .

$\cos y + 3x^3+4y=\sin x$

Possible Answers:

$\frac{\mathrm{d}y }{\mathrm{d} x}= \frac{\cos x-9x^2}{(\sin y +4 )}$

$\frac{\mathrm{d}y }{\mathrm{d} x}= \frac{(\cos x-9x^2)}{(4-\sin y )}$

$\frac{\mathrm{d}y }{\mathrm{d} x}= \frac{\cos x-9x^2}{(\sin y -4 )}$

$\frac{\mathrm{d}y }{\mathrm{d} x}= \frac{-\cos x+9x^2}{(\sin y +4y )}$

Correct answer:

$\frac{\mathrm{d}y }{\mathrm{d} x}= \frac{(\cos x-9x^2)}{(4-\sin y )}$

Explanation:

Our first step is to differentiate both sides with respect to :

$\cos y \ \frac{\mathrm{d} }{\mathrm{d} x}+ 3x^3 \frac{\mathrm{d} }{\mathrm{d} x}+4y \frac{\mathrm{d} }{\mathrm{d} x}=\sin x \frac{\mathrm{d} }{\mathrm{d} x}$

The functions of can by differentiated with respect to , just remember to multiply them by $\frac{\mathrm{d} y}{\mathrm{d} x}$ :

$-\sin y \ \frac{\mathrm{d}y }{\mathrm{d} x}+ 9x^2 +4 \frac{\mathrm{d}y }{\mathrm{d} x}=\cos x$

$-\sin y \ \frac{\mathrm{d}y }{\mathrm{d} x}+4 \frac{\mathrm{d}y }{\mathrm{d} x}=\cos x-9x^2$

$(-\sin y +4 )\frac{\mathrm{d}y }{\mathrm{d} x}=(\cos x-9x^2)$

$\frac{\mathrm{d}y }{\mathrm{d} x}= \frac{(\cos x-9x^2)}{(4-\sin y )}$

Report an Error

Example Question #4 : Implicit Differentiation

Differentiate the following with respect to .

$\cos x +xy^2-\sin y=y^2$

Possible Answers:

$\frac{\mathrm{d}y }{\mathrm{d} x} =\frac{\sin x-y^2}{xy-\cos y -y }$

$\frac{\mathrm{d}y }{\mathrm{d} x} =\frac{\cos x-y^2}{(2xy-\sin y -2y) }$

$\frac{\mathrm{d}y }{\mathrm{d} x} = \frac{-(\sin x+y^2)}{2xy-\cos y -2y }$

$\frac{\mathrm{d}y }{\mathrm{d} x} =\frac{\sin x-y^2}{(2xy-\cos y -2y) }$

Correct answer:

$\frac{\mathrm{d}y }{\mathrm{d} x} =\frac{\sin x-y^2}{(2xy-\cos y -2y) }$

Explanation:

Our first step is to differentiate both sides with respect to :

$\cos x \frac{\mathrm{d} }{\mathrm{d} x} +xy^2\ \frac{\mathrm{d} }{\mathrm{d} x}-\sin y \ \frac{\mathrm{d} }{\mathrm{d} x}=y^2 \ \frac{\mathrm{d} }{\mathrm{d} x}$

Note: we can differentiate the terms that are functions of with respect to , just remember to multiply it by $\frac{\mathrm{d} y}{\mathrm{d} x}$ .

$-\sin x +y^2 +2xy \ \frac{\mathrm{d} y}{\mathrm{d} x}-\cos y \ \frac{\mathrm{d} y}{\mathrm{d} x}=2y \ \frac{\mathrm{d}y }{\mathrm{d} x}$

Note: The product rule was applied above:

$xy^2 \ \frac{\mathrm{d} }{\mathrm{d} x}=x\frac{\mathrm{d} }{\mathrm{d} x}y^2+y^2\frac{\mathrm{d} y}{\mathrm{d} x}x=y^2+2yx\frac{\mathrm{d} y}{\mathrm{d} x}$

$2xy \ \frac{\mathrm{d} y}{\mathrm{d} x}-\cos y \ \frac{\mathrm{d} y}{\mathrm{d} x}-2y \ \frac{\mathrm{d}y }{\mathrm{d} x} =\sin x-y^2$

$(2xy-\cos y -2y) \ \frac{\mathrm{d}y }{\mathrm{d} x} =\sin x-y^2$

$\frac{\mathrm{d}y }{\mathrm{d} x} =\frac{\sin x-y^2}{(2xy-\cos y -2y) }$

Report an Error

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Tutors

Mohammed
Certified Tutor

Undergradute-University of Maryland-College Park, Bachelor of Science, Electrical Engineering. Graduate Degree-University of ...

All GRE Subject Test: Math Resources

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

Popular Subjects

SSAT Tutors in Los Angeles, ACT Tutors in Chicago, Statistics Tutors in Houston, Biology Tutors in New York City, MCAT Tutors in San Diego, GRE Tutors in San Diego, LSAT Tutors in Phoenix, GRE Tutors in Chicago, SAT Tutors in Miami, Reading Tutors in Seattle

Popular Courses & Classes

ACT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Miami, MCAT Courses & Classes in Chicago, LSAT Courses & Classes in Seattle, MCAT Courses & Classes in Washington DC, MCAT Courses & Classes in Denver, GRE Courses & Classes in Boston, SAT Courses & Classes in Denver, GRE Courses & Classes in Los Angeles

Popular Test Prep

MCAT Test Prep in Denver, MCAT Test Prep in Philadelphia, ACT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Boston, SSAT Test Prep in Boston, GRE Test Prep in Phoenix, MCAT Test Prep in Washington DC, ACT Test Prep in Miami, SSAT Test Prep in Seattle, MCAT Test Prep in Miami

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 : Implicit Differentiation

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Implicit Differentiation

Example Question #2 : Implicit Differentiation

Example Question #3 : Implicit Differentiation

Example Question #4 : Implicit Differentiation

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: