We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Derivative Review

Study concepts, example questions & explanations for Calculus 2

Create An Account

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #331 : Derivative Review

Find the derivative of the function $f(x)=2x\cos(x)$

Possible Answers:

$4x\cos(x)$

$2\cos(x)-2x\sin(x)$

$2x\cos(x)+1$

Correct answer:

$2\cos(x)-2x\sin(x)$

Explanation:

To solve, we use the product rule $\frac{\mathrm{d} }{\mathrm{d} x}f(x)g(x)=f'(x)g(x)+f(x)g'(x)$ . Applying, we get $f'(x)= (2x)'\cos(x)+2x(\cos(x))'$ . Taking the derivatives we get the correct solution $2\cos(x)-2x\sin(x)$

Report an Error

Example Question #332 : Derivative Review

What is the second derivative of f(x)=5x^2-12x+4 ?

Possible Answers:

f{}''(x)=10

f{}''(x)=10x-1

f{}''(x)=x

$f{}''(x)=10x^2$

f{}''(x)=10x

Correct answer:

f{}''(x)=10

Explanation:

To find the second derivative, you must first find the first derivative. Remember to multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:

f{}'(x)=10x-12

Now, take the derivative of the first derivative to find the second:

f{}''(x)=10 .

Report an Error

Example Question #333 : Derivative Review

What is the second derivative of f(x)=3x^3-8x^2+x-4?

Possible Answers:

$f{}''(x)=\frac{18}{x}$

f{}''(x)=18x-16

f{}''(x)=18

f{}''(x)=18x

$f{}''(x)=18x^2-16x$

Correct answer:

f{}''(x)=18x-16

Explanation:

First, find the first derivative. Remember to multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:

$f{}'(x)=9x^2-16x+1$

Now, take the second derivative:

f{}''(x)=18x-16

Report an Error

Example Question #132 : First And Second Derivatives Of Functions

What is the derivative of $f(x)=2x^{\frac{5}{4}}$ ?

Possible Answers:

$f{}'(x)=\frac{3}{2}x^{\frac{1}{4}}$

$f{}'(x)=\frac{5}{2}x^{\frac{3}{4}}$

$f{}'(x)=\frac{5}{2}x^{\frac{1}{4}}$

$f{}'(x)=\frac{5}{2}x^{\frac{1}{4}}+C$

$f{}'(x)=\frac{1}{2}x^{\frac{1}{4}}$

Correct answer:

$f{}'(x)=\frac{5}{2}x^{\frac{1}{4}}$

Explanation:

Remember that when differentiating, multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent as well.

$f{}'(x)=2(\frac{5}{4})x^{\frac{1}{4}}=\frac{10}{4}x^{\frac{1}{4}}$

Simplify to get your answer.

$f{}'(x)=\frac{5}{2}x^{\frac{1}{4}}$

Report an Error

Example Question #332 : Derivative Review

What is the derivative of f(x)=-3t^2+4t-1?

Possible Answers:

$f{}'(x)=-6t+4t^2$

f{}'(x)=-6t

f{}'(x)=-6t-4

f{}'(x)=-6t+4

f{}'(x)=6t+4

Correct answer:

f{}'(x)=-6t+4

Explanation:

To take the derivative, remember to multiply the exponent by the coefficient in front of the x term:

f{}'(x)=-6t+4

Report an Error

Example Question #136 : First And Second Derivatives Of Functions

What is the second derivative of f(x)=4x^3-2x+6 ?

Possible Answers:

f{}''(x)=24x

f{}''(x)=24x+2

f{}''(x)=4x

f{}''(x)=24

f{}''(x)=24x+C

Correct answer:

f{}''(x)=24x

Explanation:

Before you can take the second derivative, you must take the first derivative. Remember to multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:

$f{}'(x)=12x^2-2$

Now, take the derivative of this to find the second derivative:

f{}''(x)=24x

Report an Error

Example Question #333 : Derivative Review

What is the derivative of f(x)=5x^3-2x^2+4x?

Possible Answers:

$f{}'(x)=15x^2-4x$

$f{}'(x)=15x^2+2x+4$

$f{}'(x)=-15x^2-4x+4$

$f{}'(x)=15x^2-4x+4$

$f{}'(x)=15x^2-4x-4$

Correct answer:

$f{}'(x)=15x^2-4x+4$

Explanation:

To take the derivative, remember to multiply the exponent by the coefficient and then subtract one from the exponent:

$f{}'(x)=15x^2-4x+4$

Report an Error

Example Question #335 : Derivatives

What is the derivative of $f(x)=9x^{\frac{2}{3}}-4x^2+x$ ?

Possible Answers:

$f{}'(x)=\frac{6}{x^{\frac{1}{3}}}-8x+1$

$f{}'(x)=\frac{6}{x^{\frac{1}{3}}}-8x-1$

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

$f{}'(x)=\frac{6}{x^{\frac{1}{3}}}-8x$

$f{}'(x)=\frac{6}{x^{\frac{2}{3}}}-8x+1$

Correct answer:

$f{}'(x)=\frac{6}{x^{\frac{1}{3}}}-8x+1$

Explanation:

Remember that when taking the derivative, multiply the exponent by the coefficient and then subtract one from the exponent:

$f{}'(x)=6x^{\frac{-1}{3}}-8x+1$

Simplify so you don't have a negative exponent:

$f{}'(x)=\frac{6}{x^{\frac{1}{3}}}-8x+1$

Report an Error

Example Question #334 : Derivative Review

Find the derivative of the given function

f(x)=x^x

Possible Answers:

$x^{x-1}\ln(x-1)$

$x^x(1+\ln(\ln x))$

$x^x\ln(1+\ln x)$

$x^x(1+\ln x)$

Correct answer:

$x^x(1+\ln x)$

Explanation:

Untitled

Report an Error

Example Question #140 : First And Second Derivatives Of Functions

Find the first derivative of the following function: $y=lnxcos(e^{x})$

Possible Answers:

$\frac{\mathrm{dy} }{\mathrm{d} x}=\frac{sin(e^{x})}{x}-e^{x}lnxsin(e^{x})$

$\frac{\mathrm{dy} }{\mathrm{d} x}=\frac{cos(e^{x})}{x}-e^{x}lnxsin(e^{x})$

$\frac{\mathrm{dy} }{\mathrm{d} x}=lnxsinxe^{x}$

$\frac{\mathrm{dy} }{\mathrm{d} x}=lnxcos(e^{x})+\frac{cosx}{x}$

Correct answer:

$\frac{\mathrm{dy} }{\mathrm{d} x}=\frac{cos(e^{x})}{x}-e^{x}lnxsin(e^{x})$

Explanation:

To solve this problem, we use a combination of the product and chain rules. First, we use the product rule, which looks like this:

$\frac{\mathrm{dy} }{\mathrm{d} x}=lnx\frac{\mathrm{d} }{\mathrm{d} x}cos(e^{x})+\frac{\mathrm{d} }{\mathrm{d} x}lnxcos(e^{x})$ , which simplifies to:

$\frac{dy}{dx}=lnx\frac{d}{dx}cos(e^{x})+\frac{cos(e^{x})}{x}$ . We need to use the chain rule to find the derivative of $cos(e^{x})$ , which looks like this:

$\frac{d}{dx}cos(e^{x})=-sin(e^{x})e^{x}$ . Plugging this back into our equation above, we get:

$\frac{dy}{dx}=-lnxsin(e^{x})e^{x}+\frac{cos(e^{x})}{x}$ , which simplifies to:

$\frac{dy}{dx}=\frac{cos(e^{x})}{x}-e^{x}lnxsin(e^{x})$

Report an Error

View Calculus 2 Tutors

Yoonsik
Certified Tutor

Seoul National University, Bachelor of Science, Physics. University of Pennsylvania, Doctor of Philosophy, Atomic and Molecul...

View Calculus 2 Tutors

Jason
Certified Tutor

Brigham Young University, Bachelor, Neuroscience.

View Calculus 2 Tutors

Nicole
Certified Tutor

College of St Benedict, Bachelor in Arts, Economics. University of South Florida-Main Campus, Master of Arts, Economics.

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Seattle, English Tutors in Houston, MCAT Tutors in Denver, Biology Tutors in San Francisco-Bay Area, Algebra Tutors in Washington DC, SAT Tutors in Atlanta, ACT Tutors in Phoenix, GMAT Tutors in New York City, ISEE Tutors in San Diego, Reading Tutors in Dallas Fort Worth

Popular Courses & Classes

GRE Courses & Classes in Washington DC, ISEE Courses & Classes in Chicago, LSAT Courses & Classes in Houston, GMAT Courses & Classes in Atlanta, SAT Courses & Classes in Chicago, GMAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Phoenix, ISEE Courses & Classes in Miami, GRE Courses & Classes in Houston, SAT Courses & Classes in Boston

Popular Test Prep

GMAT Test Prep in Atlanta, GMAT Test Prep in Houston, LSAT Test Prep in Los Angeles, SAT Test Prep in Miami, ACT Test Prep in Miami, ISEE Test Prep in Miami, LSAT Test Prep in Washington DC, LSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Denver, LSAT Test Prep in New York City

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 2 : Derivative Review

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #331 : Derivative Review

Example Question #332 : Derivative Review

Example Question #333 : Derivative Review

Example Question #132 : First And Second Derivatives Of Functions

Example Question #332 : Derivative Review

Example Question #136 : First And Second Derivatives Of Functions

Example Question #333 : Derivative Review

Example Question #335 : Derivatives

Example Question #334 : Derivative Review

Example Question #140 : First And Second Derivatives Of Functions

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: