We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 1 : How to find differential functions

Study concepts, example questions & explanations for Calculus 1

Create An Account

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 … 79 80 81 82 83 84 85 86 87 Next →

Example Question #851 : How To Find Differential Functions

Find the first derivative of the following function:

f(x)= 3x^2+2x+1

Possible Answers:

f'(x)= 5x+ 3

f'(x)= 6x+1

f'(x)= 6x+3

f'(x)= 6x+2

Correct answer:

f'(x)= 6x+2

Explanation:

To find the first derivative of this particular function is accomplished by applying the power rule which states,

$\frac{\mathrm{d} }{\mathrm{d} x}x^n= n(x)^{n-1}$

Applying the above rule to the equation,

f(x)= 3x^2+2x+1

results in,

$\\f'(x)= 2\cdot 3x^{2-1}+1\cdot 2x^{1-1} \\f'(x)=6x^1+2x^0$

f'(x)= 6x+2

Report an Error

Example Question #852 : How To Find Differential Functions

Find the first derivative of the function $f(x)= 4x^2 + \sin(2x)$ .

Possible Answers:

$f'(x)= 8x-\cos(2x)$

$f'(x)= 8x-2\cos(2x)$

$f'(x)= 8x+ 2\cos(2x)$

$f'(x)= 8x-2\sin(2x)$

Correct answer:

$f'(x)= 8x+ 2\cos(2x)$

Explanation:

To take the derivative, you first use the power rule for differentiating,

$\frac{\mathrm{d} }{\mathrm{d} x}x^n= nx^{n-1}$ ,

then you use the chain rule,

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

Also recall the trigonometric rule for differentiating sine,

$(sin(u))'=cos(u)\frac{du}{dx}$

This produces,

$f'(x)= 2\cdot 4x^{2-1} + \cos(2x)\cdot 1\cdot2x^{1-1}$

$f'(x)= 8x +2\cos(2x)$ .

Report an Error

Example Question #853 : How To Find Differential Functions

Find the derivative.

$\frac{4x^2+3x}{x^3}$

Possible Answers:

$\frac{8x^4-9}{x^4}$

$\frac{8x^4-9}{x^6}$

$\frac{-4x-6}{x^3}$

$\frac{8x^4+3x^3-12x^2-9}{x^4}$

Correct answer:

$\frac{-4x-6}{x^3}$

Explanation:

Use the quotient rule to find the derivative which states,

$\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{g(x)^2}$ .

Given,

f(x)=4x^2+3x

g(x)=x^3

the derivatives can be found using the power rule which states,

$\frac{d}{dx}x^n=nx^{n-1}$

therefore,

$\\ f'(x)=2\cdot 4x^{2-1}+1\cdot 3x^{1-1}=8x+3 \\g'(x)=3x^{3-1}=3x^2$

Applying the quotient rule to our function we find the derivative to be as follows.

$\frac{d}{dx}\frac{4x^2+3x}{x^3}=\frac{x^3(8x+3)-(4x^2+3x)3x^2}{x^6}$

Simplify.

$\frac{8x^4+3x^3-12x^4-9x^3}{x^6}$

$\frac{-4x^4-6x^3}{x^6}$

$\frac{x^3(-4x-6)}{x^3(x^3)}=\frac{-4x-6}{x^3}$

Report an Error

Example Question #851 : How To Find Differential Functions

Find the derivative.

-4x^3

Possible Answers:

-4x^2

4x^3

12x^2

-12x^2

Correct answer:

-12x^2

Explanation:

Use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying this rule to the function in the problem results in the following.

$\frac{d}{dx}(-4x^3)=3(-4)x^{3-1}=-12x^2$

Report an Error

Example Question #852 : How To Find Differential Functions

Find the derivative.

4x-3

Possible Answers:

-4x

Correct answer:

Explanation:

Use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying this rule to each term of the function results in the following.

$\frac{d}{dx}4x=4$

$\frac{d}{dx}-3=0$

Thus, the derivative is 4.

Report an Error

Example Question #856 : How To Find Differential Functions

What is the equation for the slope of the tangent line to:

8x^2-4x+4

Possible Answers:

8x-4

16x-4

16x+4

8x+4

Correct answer:

16x-4

Explanation:

To find the equation for the slope of the tangent line, find the derivative.

To find the derivative, use the power rule.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying the power rule to each term in the function results in,

$\frac{d}{dx}8x^2=16x$

$\frac{d}{dx}-4x=-4$

$\frac{d}{dx}4=0$ .

Thus, the derivative is 16x-4 .

Report an Error

Example Question #1041 : Differential Functions

Find the derivative when x=3 .

x^3+5x^2

Possible Answers:

Correct answer:

Explanation:

Use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying the power rule to each term within the function results in the following.

$\frac{d}{dx}x^3=3x^2$

$\frac{d}{dx}5x^2=10x$

Thus, the derivative is 3x^2+10x

Now, substitute for .

3(3^2)+10(3)=57

Report an Error

Example Question #858 : How To Find Differential Functions

Find the derivative when x=2 .

5x^2-3x

Possible Answers:

Correct answer:

Explanation:

First, use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying the power rule to each term in the function results in the following.

$\frac{d}{dx}5x^2=10x$

$\frac{d}{dx}-3x=-3$

Thus, the derivative is 10x-3 .

Now, substitute 2 for x.

10(2)-3=17 .

Report an Error

Example Question #859 : How To Find Differential Functions

Find the derivative.

$2x\cos (x)$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Use the product rule to find the derivative.

The product rule states,

$\frac{d}{dx}f(x)g(x)=f(x)g'(x)+g(x)f'(x)$ .

Given,

f(x)=2x

g(x)=cos(x)

and recalling the trigonometry derivative for cosine is,

$\frac{d}{dx}cos(x)=-sin(x)$

the derivatives are as follows.

$f'(x)=1\cdot 2x^{1-1}=2$

g'(x)=-sin(x)

Therefore, using the product rule the derivative becomes,

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

Report an Error

Example Question #851 : Other Differential Functions

Find the derivative.

2x^4-x^3

Possible Answers:

8x^3+3x^2

8x^3-x^2

8x^3+x^2

8x^3-3x^2

Correct answer:

8x^3-3x^2

Explanation:

Use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying the power rule to each term in the function results in the following.

$\frac{d}{dx}2x^4=8x^3$

$\frac{d}{dx}(-x^3)=-3x^2$ .

Thus, the derivative is 8x^3-3x^2 .

Report an Error

← Previous 1 2 … 79 80 81 82 83 84 85 86 87 Next →

View Calculus Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Calculus Tutors

Epiphany
Certified Tutor

University of Rochester, Bachelor in Arts, Economics.

View Calculus Tutors

Dr. Derrick
Certified Tutor

Huston-Tillotson University, Bachelor of Science, Mathematics. Grand Canyon University, Master of Arts, Education.

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in Chicago, Statistics Tutors in Atlanta, Computer Science Tutors in San Francisco-Bay Area, MCAT Tutors in New York City, ISEE Tutors in San Diego, ACT Tutors in Houston, MCAT Tutors in San Diego, SAT Tutors in Atlanta, GMAT Tutors in Washington DC, Computer Science Tutors in New York City

Popular Courses & Classes

MCAT Courses & Classes in Boston, LSAT Courses & Classes in Phoenix, Spanish Courses & Classes in Miami, SAT Courses & Classes in New York City, ACT Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Boston, Spanish Courses & Classes in Boston, MCAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Miami

Popular Test Prep

LSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Los Angeles, GRE Test Prep in Atlanta, MCAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Seattle, ACT Test Prep in Boston, GMAT Test Prep in Atlanta, LSAT Test Prep in Atlanta, LSAT Test Prep in Philadelphia, LSAT 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 1 : How to find differential functions

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #851 : How To Find Differential Functions

Example Question #852 : How To Find Differential Functions

Example Question #853 : How To Find Differential Functions

Example Question #851 : How To Find Differential Functions

Example Question #852 : How To Find Differential Functions

Example Question #856 : How To Find Differential Functions

Example Question #1041 : Differential Functions

Example Question #858 : How To Find Differential Functions

Example Question #859 : How To Find Differential Functions

Example Question #851 : Other Differential Functions

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: