We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

Create An Account

All Calculus 3 Resources

6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #411 : Partial Derivatives

Given the function $f(x,y)=5x^2y^2+10xy+20x^3y^{3/2}$ , find the partial derivative f_x .

Possible Answers:

$f_x=10x^2y^2+10y+60x^2y^{3/2}$

$f_x=5xy^2+10y+20x^3y^{3/2}$

$f_x=10xy^2+10x+60x^2y^{3/2}$

$f_x=10xy^2+10y+60x^2y^{3/2}$

Correct answer:

$f_x=10xy^2+10y+60x^2y^{3/2}$

Explanation:

To find the partial derivative f_x of $f(x,y)=5x^2y^2+10xy+20x^3y^{3/2}$ , we take the derivative with respect to while holding constant. So we have

$f_x=\frac{\partial}{\partial x}f(x,y)=\frac{\partial}{\partial x}(5x^2y^2+10xy+20x^3y^{3/2})$

$=\frac{\partial}{\partial x}5x^2y^2+\frac{\partial}{\partial x}10xy+\frac{\partial}{\partial x}20x^3y^{3/2}$

$=10xy^2+10y+60x^2y^{3/2}$

Report an Error

Example Question #412 : Partial Derivatives

Find the partial derivative f_y of the function $f(x,y)=5x^2y^2+10xy+20x^3y^{3/2}$ .

Possible Answers:

$f_y=10x^2y+10y+30x^3y^{1/2}$

$f_y=10x^2y+10y+60x^3y^{1/2}$

$f_y=10x^2y+10x+30x^3y^{1/2}$

$f_y=10x^2y^2+10x+30x^3y^{1/2}$

Correct answer:

$f_y=10x^2y+10x+30x^3y^{1/2}$

Explanation:

To find the partial derivative f_y of $f(x,y)=5x^2y^2+10xy+20x^3y^{3/2}$ , we take the derivative with respect to while holding constant. So we have

$f_y=\frac{\partial}{\partial y}f(x,y)=\frac{\partial}{\partial y}(5x^2y^2+10xy+20x^3y^{3/2})$

$=\frac{\partial}{\partial y}5x^2y^2+\frac{\partial}{\partial y}10xy+\frac{\partial}{\partial y}20x^3y^{3/2}$

$=10x^2y+10x+30x^3y^{1/2}$

Report an Error

Example Question #413 : Partial Derivatives

Find the value of f_x for f(x,y)=4x^2+3y^3 at (-2,5)

Possible Answers:

225

209

Correct answer:

Explanation:

Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, $\delta$ , or by the subscript of the variable being considered such as f_x or f_y .

Taking the partial derivative of f(x,y)=4x^2+3y^3 at (-2,5)

We find:

$f_x= 8x+0\rightarrow-16$

Report an Error

Example Question #414 : Partial Derivatives

Find the value of f_x for f(x,y)=2x^3y+4x at (2,3)

Possible Answers:

Correct answer:

Explanation:

Taking the partial derivative of f(x,y)=2x^3y+4x at (2,3)

We find:

$f_x=6x^2y+4 \rightarrow72+4=76$

Report an Error

Example Question #415 : Partial Derivatives

Find the value of f_x for f(x,y)=ln(x^2)cos(y) at $(2,\pi)$

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

Knowledge of the following derivative rules will be necessary:

Derivative of a natural log:

$d[ln(u)]=\frac{du}{u}$

Note that u may represent large functions, and not just individual variables!

Taking the partial derivative of f(x,y)=ln(x^2)cos(y) at $(2,\pi)$

We find:

$f_x=\frac{2cos(y)}{x} \rightarrow-1$

Report an Error

Example Question #416 : Partial Derivatives

F(x,y)=3x^3+x^2y+3xy^2+5y^3

Find $\frac{\partial F }{\partial x}$

Possible Answers:

$\frac{\partial F}{\partial x}=9x^2+2xy+3y^2$

$\frac{\partial F}{\partial x}=x^2+6xy+15y^2$

$\frac{\partial F}{\partial x}=5y^3$

Correct answer:

$\frac{\partial F}{\partial x}=9x^2+2xy+3y^2$

Explanation:

$\frac{\partial F }{\partial x}$ is defined as the partial derivative of taken with respect to . Any other variable is treated as a constant.

Finding the partial derivative with respect to ,

$\frac{\partial F }{\partial x}=\frac{\partial }{\partial x}[F(x,y)]$

$=\frac{\partial }{\partial x}(3x^3+x^2y+3xy^2+5y^3)$

We use the power rule on x as we take the derivative and find that

$=3*3x^{3-1}+2*x^{2-1}y+1*3x^{1-1}y^2+0*5y^3x^{0-1}$

As such

$\frac{\partial F}{\partial x}=9x^2+2xy+3y^2$

Report an Error

Example Question #417 : Partial Derivatives

Find the value of f_x for f(x,y)=cos(xy) at $(\pi,\frac{3}{2})$

Possible Answers:

$\pi$

$\frac{3}{2}$

$-\frac{3}{2}$

$-\pi$

Correct answer:

$\frac{3}{2}$

Explanation:

Knowledge of the following derivative rules will be necessary:

Trigonometric derivative:

d[cos(u)]=-sin(u)du

Note that u may represent large functions, and not just individual variables!

Taking the partial derivative of f(x,y)=cos(xy) at $(\pi,\frac{3}{2})$

We find:

$f_x= -ysin(xy)\rightarrow\frac{3}{2}$

Report an Error

Example Question #418 : Partial Derivatives

Given f(x,y,z,w) = xyzw+(xyzw)^2 , find $f_{xw}$

Possible Answers:

2xyzw

None of the other answers

xw+4xw

yz+4xy^2z^2w

yz+y^2z^2

Correct answer:

yz+4xy^2z^2w

Explanation:

To find $f_{xw}$ , first we take the partial derivative with respect to , keeping the other variables constant (i.e. treating the other variables as numbers)

So the partial derivative of with respect to is

f_x = yzw +2(xyzw)yzw =yzw +2xy^2z^2w^2 .

Now we take the partial derivative of f_x with respect to , keeping the other variables constant.

$f_{xw} = yz+4xy^2z^2w$ .

Report an Error

Example Question #421 : Partial Derivatives

F(x,y)=cos (x) + sin (y) -x^2+xy-y^2

Find $\frac{\partial F}{\partial y}$

Possible Answers:

$\frac{\partial F}{\partial y}=cos (y) +x-2y$

$\frac{\partial F}{\partial y}=-sin(x)-2x+y$

$\frac{\partial F}{\partial y}=cos (x) -x^2$

Correct answer:

$\frac{\partial F}{\partial y}=cos (y) +x-2y$

Explanation:

$\frac{\partial F }{\partial y}$ is defined as the partial derivative of taken with respect to . Any other variable is treated as a constant.

Finding the partial derivative with respect to ,

$\frac{\partial F }{\partial y}=\frac{\partial }{\partial y}[F(x,y)]$

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

We use the power rule on and the definition of trigonometric derivatives as we take the derivative and find that

$=0*cos(x)y^{0-1}+cos(y)-0*x^2y^{0-1}+1*xy^{1-1}-2*y^{2-1}$

As such

$\frac{\partial F}{\partial y}=cos (y) +x-2y$

Report an Error

Example Question #2781 : Calculus 3

Find the value of f_x for $f(x,y)=e^{x^2y}+5x$ at (2,2)

Possible Answers:

4e^4+5

e^4+5

4e^8+5

8e^8+5

8e^4+5

Correct answer:

8e^8+5

Explanation:

Knowledge of the following derivative rules will be necessary:

Derivative of an exponential:

d[e^u]=e^udu

Note that u may represent large functions, and not just individual variables!

Taking the partial derivative of $f(x,y)=e^{x^2y}+5x$ at (2,2)

We find:

$f_x=2xye^{x^2y}+5 \rightarrow8e^8+5$

Report an Error

View Calculus 3 Tutors

David
Certified Tutor

The University of Texas at El Paso, Bachelor of Science, Computational Mathematics. Indiana State University, Master of Scien...

View Calculus 3 Tutors

Sumit
Certified Tutor

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

View Calculus 3 Tutors

Robert
Certified Tutor

Rensselaer Polytechnic Institute, Bachelors, Electrical Engineering. Brooklyn Polytechnic, Masters, Computer Science.

All Calculus 3 Resources

6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Miami, English Tutors in Phoenix, Computer Science Tutors in Phoenix, SSAT Tutors in Los Angeles, Statistics Tutors in Philadelphia, Computer Science Tutors in Miami, Math Tutors in Dallas Fort Worth, English Tutors in Dallas Fort Worth, Chemistry Tutors in Los Angeles, SAT Tutors in Dallas Fort Worth

Popular Courses & Classes

LSAT Courses & Classes in Chicago, GRE Courses & Classes in Seattle, MCAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Washington DC, SSAT Courses & Classes in Seattle, LSAT Courses & Classes in Los Angeles, ISEE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Phoenix, Spanish Courses & Classes in Dallas Fort Worth

Popular Test Prep

GMAT Test Prep in Dallas Fort Worth, GRE Test Prep in Boston, LSAT Test Prep in Washington DC, SAT Test Prep in Los Angeles, ACT Test Prep in San Francisco-Bay Area, SAT Test Prep in Dallas Fort Worth, SAT Test Prep in Boston, MCAT Test Prep in Seattle, GMAT Test Prep in Boston, LSAT 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

Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #411 : Partial Derivatives

Example Question #412 : Partial Derivatives

Example Question #413 : Partial Derivatives

Example Question #414 : Partial Derivatives

Example Question #415 : Partial Derivatives

Example Question #416 : Partial Derivatives

Example Question #417 : Partial Derivatives

Example Question #418 : Partial Derivatives

Example Question #421 : Partial Derivatives

Example Question #2781 : Calculus 3

All Calculus 3 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: