Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 3 : Partial Derivatives

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 #401 : Partial Derivatives

Given the function $f(x,y,z)=5e^{x+y+xyz}$ , find the partial derivative f_x(x,y,z)

Possible Answers:

$f_x(x,y,z)=5(1+yz)e^{x+y+xyz}$

$f_x(x,y,z)=5(1+xz)e^{x+y+xyz}$

$f_x(x,y,z)=5yze^{x+y+xyz}$

Correct answer:

$f_x(x,y,z)=5(1+yz)e^{x+y+xyz}$

Explanation:

We can find the partial derivative f_x(x,y,z) of the function $f(x,y,z)=5e^{x+y+xyz}$ by taking its derivative with respect to while holding and constant. We will also use the chain rule:

$f_x(x,y,z)=\frac{\partial}{\partial x}5e^{x+y+xyz}=5e^{x+y+xyz}\frac{\partial}{\partial x}(x+y+xyz)$

$=5(1+yz)e^{x+y+xyz}$

Report an Error

Example Question #2762 : Calculus 3

Given the function $f(x,y,z)=5e^{x+y+xyz}$ , find the partial derivative f_y(x,y,z)

Possible Answers:

$f_y(x,y,z)=5(1+xz)e^{x+y+xyz}$

$f_y(x,y,z)=5(1+yz)e^{x+y+xyz}$

$f_y(x,y,z)=5xze^{x+y+xyz}$

$f_y(x,y,z)=5(1+xy)e^{x+y+xyz}$

Correct answer:

$f_y(x,y,z)=5(1+xz)e^{x+y+xyz}$

Explanation:

We can find the partial derivative f_y(x,y,z) of the function $f(x,y,z)=5e^{x+y+xyz}$ by taking its derivative with respect to and holding x,z constant. We also use the chain rule to get:

$f_y(x,y,z)=\frac{\partial}{\partial y}5e^{x+y+xyz}=5e^{x+y+xyz}\frac{\partial}{\partial y}(x+y+xyz)$

$=5(1+xz)e^{x+y+xyz}$

Report an Error

Example Question #2771 : Calculus 3

Given the function $f(x,y,z)=5e^{x+y+xyz}$ , find the partial derivative f_z(x,y,z) f_y(x,y,z)

Possible Answers:

$f_z(x,y,z)=5(1+xy)e^{x+y+xyz}$

$f_z(x,y,z)=5xye^{x+y+xyz}$

$f_z(x,y,z)=5(1+yz)e^{x+y+xyz}$

$f_z(x,y,z)=5xze^{x+y+xyz}$

Correct answer:

$f_z(x,y,z)=5xye^{x+y+xyz}$

Explanation:

We can find the partial derivative f_z(x,y,z) f_y(x,y,z) of the function $f(x,y,z)=5e^{x+y+xyz}$ by taking its derivative with respect to and holding x,y constant. We also use the chain rule to get:

$f_z(x,y,z)=\frac{\partial}{\partial z}5e^{x+y+xyz}=5e^{x+y+xyz}\frac{\partial}{\partial z}(x+y+xyz)$

$=5xye^{x+y+xyz}$

Report an Error

Example Question #401 : Partial Derivatives

Given the function f(x,y,z)=xy+xz+yz , find the partial derivative

f_x(x,y,z)

Possible Answers:

f_x(x,y,z)=x+y+z

f_x(x,y,z)=x+z

f_x(x,y,z)=y+z

f_x(x,y,z)=xy+xz

Correct answer:

f_x(x,y,z)=y+z

Explanation:

We can find the partial derivative f_x(x,y,z) of the function f(x,y,z)=xy+xz+yz by taking the derivative with respect to and holding and constant:

$f_x(x,y,z)=\frac{\partial}{\partial x}(xy+xz+yz)=y+z$

Report an Error

Example Question #2771 : Calculus 3

Given the function $\small f(x,y)=x^2+2xy+y^2+10$ , calculate $\small f_x(x,y)$ .

Possible Answers:

$\small \small f_x(x,y)=2x+2y$

$\small \small \small f_x(x,y)=2y+10$

$\small \small \small f_x(x,y)=2x+2y+10$

$\small \small \small f_x(x,y)=4x$

Correct answer:

$\small \small f_x(x,y)=2x+2y$

Explanation:

To find the partial derivative $\small f_x(x,y)$ of the function $\small f(x,y)=x^2+2xy+y^2+10$

we differentiate it with respect to $\small x$ while holding $\small y$ constant:

$\small \small f_x(x,y)=\frac{\partial}{\partial x}f(x,y)=\frac{\partial}{\partial x}(x^2+2xy+y^2+10)$

$\small =2x+2y$

Report an Error

Example Question #401 : Partial Derivatives

Given the function $\small f(x,y)=x^2+2xy+y^2+10$ , calculate $\small \small f_y(x,y)$ .

Possible Answers:

$\small \small \small \small f_x(x,y)=2y+2x$

$\small \small \small \small f_x(x,y)=2x+2y^2$

$\small \small \small f_x(x,y)=2x+2y+10$

$\small \small \small \small f_x(x,y)=4y$

Correct answer:

$\small \small \small \small f_x(x,y)=2y+2x$

Explanation:

To find the partial derivative $\small \small f_y(x,y)$ of the function $\small f(x,y)=x^2+2xy+y^2+10$

we differentiate it with respect to $\small y$ while holding $\small x$ constant:

$\small \small \small f_y(x,y)=\frac{\partial}{\partial y}f(x,y)=\frac{\partial}{\partial y}(x^2+2xy+y^2+10)$

$\small \small \small =2y+2x$

Report an Error

Example Question #402 : Partial Derivatives

If $f(x,y,z) = xyze^{xy}$ , find $f^{xz}$ .

Possible Answers:

$ye^{xy}$

None of the other answers

$ze^{xy}$

$xye^{xy}$

Correct answer:

None of the other answers

Explanation:

The correct answer is $(xy+1)ye^{xy}$ .

First we find f^z . ( f^x could be found first, it does not matter, but f^z avoids the product rule in the first step.)

$f(x,y,z) = xye^{xy}z$

$f^z = xye^{xy}$

Now taking the partial derivative of f^z with respect to , we obtain after using the product rule-

$f^{zx} = f^{xz} = (xy)(ye^{xy})+(y)(e^{xy}) = (xy+1)ye^{xy}$ .

Report an Error

Example Question #403 : Partial Derivatives

Given $f(x,y) = xy+e^{xy}$ , find f^x .

Possible Answers:

$y+ye^{xy}$

None of the other answers

$y+xe^{xy}$

$xy' +y + (xy'+y)e^{xy}$

Correct answer:

$y+ye^{xy}$

Explanation:

To find f^x , we take the derivative of f(x,y) , using as the variable, and treating as a constant, or a number.

This means the partial derivative of with respect to is (Similar to the derivative of being , for example.)

The partial derivative of $e^{xy}$ with respect to is therefore $ye^{xy}$ , using the Chain Rule from 1-dimensional calculus.

Putting these together, we have $f^x = y+ye^{xy}$ .

Report an Error

Example Question #407 : Partial Derivatives

Find the partial derivative f_x of the function f(x,y)=5xy+6x+2y .

Possible Answers:

f_x=5x+6

f_x=5y+2

f_x=5y+6

f_x=6

Correct answer:

f_x=5y+6

Explanation:

To find the partial derivative f_x of the function f(x,y)=5xy+6x+2y , we find its derivative with respect to while holding constant. We have

$f_x=\frac{\partial}{\partial x}f(x,y)=\frac{\partial}{\partial x}(5xy+6x+2y)=\frac{\partial}{\partial x}5xy+\frac{\partial}{\partial x}6x+\frac{\partial}{\partial x}2y$

=5y+6+0=5y+6

Report an Error

Example Question #408 : Partial Derivatives

Find the partial derivative f_y of the function f(x,y)=5xy+6x+2y .

Possible Answers:

f_y=5x+2

f_y=5x+6

f_y=5y+2

f_y=2

Correct answer:

f_y=5x+2

Explanation:

To find the partial derivative f_y of the function f(x,y)=5xy+6x+2y , we find its derivative with respect to while holding constant. We have

$f_y=\frac{\partial}{\partial y}f(x,y)=\frac{\partial}{\partial y}(5xy+6x+2y)=\frac{\partial}{\partial y}5xy+\frac{\partial}{\partial y}6x+\frac{\partial}{\partial y}2y$

=5x+0+2=5x+2

Report an Error

View Calculus 3 Tutors

Cole
Certified Tutor

Louisiana State University-Alexandria, Bachelor of Science, Computer Engineering, General. Louisiana State University-Alexand...

View Calculus 3 Tutors

Garth
Certified Tutor

View Calculus 3 Tutors

Jan
Certified Tutor

University of Connecticut, Bachelor of Science, Computer Science.

All Calculus 3 Resources

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

Popular Subjects

Spanish Tutors in San Diego, Algebra Tutors in Philadelphia, Computer Science Tutors in Houston, Algebra Tutors in Seattle, Physics Tutors in Philadelphia, Reading Tutors in Atlanta, Algebra Tutors in Denver, LSAT Tutors in San Francisco-Bay Area, SAT Tutors in Los Angeles, Algebra Tutors in New York City

Popular Courses & Classes

GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in Boston, GMAT Courses & Classes in Denver, GRE Courses & Classes in Chicago, GMAT Courses & Classes in Houston, MCAT Courses & Classes in Washington DC, ACT Courses & Classes in Boston, MCAT Courses & Classes in Miami, SAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

GMAT Test Prep in Miami, GMAT Test Prep in Phoenix, SSAT Test Prep in Miami, ACT Test Prep in San Diego, LSAT Test Prep in Washington DC, MCAT Test Prep in Seattle, LSAT Test Prep in Chicago, LSAT Test Prep in Los Angeles, LSAT Test Prep in Houston, SAT Test Prep in Washington DC

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 : Partial Derivatives

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #401 : Partial Derivatives

Example Question #2762 : Calculus 3

Example Question #2771 : Calculus 3

Example Question #401 : Partial Derivatives

Example Question #2771 : Calculus 3

Example Question #401 : Partial Derivatives

Example Question #402 : Partial Derivatives

Example Question #403 : Partial Derivatives

Example Question #407 : Partial Derivatives

Example Question #408 : Partial Derivatives

All Calculus 3 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: