Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Find the First Derivative of a Function

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #132 : Introductory Calculus

Find the first derivative of the following function:

$\displaystyle f(x)=5x-7x^2-2$

Possible Answers:

$\displaystyle f'(x)=5+14x$

$\displaystyle f'(x)=-14x+5$

$\displaystyle f'(x)=5x-7x^2-2$

$\displaystyle f'(x)=5x+14$

Correct answer:

$\displaystyle f'(x)=-14x+5$

Explanation:

To solve, simply differentiate using the power rule for differentiation as outline below.

$(x^n)^{'}=nx^{n-1}$ $\displaystyle (x^n)^{'}=nx^{n-1}$

Thus,

$f'(x)=5x^{1-1}-7x^{2-1}$ $\displaystyle f'(x)=5x^{1-1}-7x^{2-1}$

Notice that our constant term disappeared because the derivative of a constant is zero.

Simplifying the above equation, we get:

$\displaystyle f'(x)=5x^0-7x^1=5-7x$

Thus, our answer is:

$\displaystyle f'(x)=5-7x$

Report an Error

Example Question #41 : Find The First Derivative Of A Function

Find the first derivative of the following equation:

$\displaystyle f(x)=x^2+77x-1$

Possible Answers:

2x+7 $\displaystyle 2x+7$

$\displaystyle 2$

2x+77 $\displaystyle 2x+77$

$\displaystyle 0$

Correct answer:

2x+77 $\displaystyle 2x+77$

Explanation:

To solve, simply use the power rule as outline below:

Power rule: $(x^n)'=nx^{n-1}$ $\displaystyle (x^n)'=nx^{n-1}$

Thus,

$f'(x)=2x^{2-1}+77x^{1-1}=2x+77$ $\displaystyle f'(x)=2x^{2-1}+77x^{1-1}=2x+77$

Report an Error

Example Question #41 : Find The First Derivative Of A Function

Find the first derivative of the following function:

$\displaystyle f(x)=(2x+1)(x^2-3)$

Possible Answers:

$\displaystyle f'(x)=2x^3+x^2-6x-3$

$\displaystyle f(x)=(2x-1)(2x)-(2)(x^2-3)$

$\displaystyle 0$

$\displaystyle f'(x)=6x^2+2x-6$

Correct answer:

$\displaystyle f'(x)=6x^2+2x-6$

Explanation:

To solve, you must use the product rule as outline below.

Product rule: $\displaystyle (g(x)*h(x))'=g(x)h'(x)+g'(x)h(x)$

$g(x)=(2x+1)\rightarrow g'(x)=2$ $\displaystyle g(x)=(2x+1)\rightarrow g'(x)=2$

$h(x)=(x^2-3)\rightarrow h'(x)=2x$ $\displaystyle h(x)=(x^2-3)\rightarrow h'(x)=2x$

Thus,

$\displaystyle f'(x)=(2x+1)(2x)+(2)(x^2-3)$

Distribute the 2x and 2.

$\displaystyle f'(x)=4x^2+2x+2x^2-6$

Combine like terms to simplify.

$\displaystyle f'(x)=6x^2+2x-6$

Report an Error

Example Question #758 : Pre Calculus

Find the first derivative of the function $f(x) = \frac{1}{x}$ $\displaystyle f(x) = \frac{1}{x}$ .

Possible Answers:

$f(x) = -\sqrt{x}$ $\displaystyle f(x) = -\sqrt{x}$

$\displaystyle f(x) = ln(x)$

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

Correct answer:

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

Explanation:

An equivalent form of writing $f(x) = \frac{1}{x}$ $\displaystyle f(x) = \frac{1}{x}$ is $f(x) = x^{-1}$ $\displaystyle f(x) = x^{-1}$ . The derivative of an exponential power x^b $\displaystyle x^b$ is $bx^{b-1}$ $\displaystyle bx^{b-1}$ , so the derivative of $f(x) = x^{-1}$ $\displaystyle f(x) = x^{-1}$ is $f'(x) = -x^{-2}$ $\displaystyle f'(x) = -x^{-2}$ , or $f'(x) = \frac{-1}{x^2}$ $\displaystyle f'(x) = \frac{-1}{x^2}$ .

Report an Error

Example Question #759 : Pre Calculus

Find the first derivative: $\displaystyle 12x^4-3x^3+2x^2-12-6x-9x^3$

Possible Answers:

None of the other answers.

$\displaystyle 12x^3-3x^2+4x-18$

$\displaystyle 48x^3-36x^2+4x+18$

$\displaystyle 48x^3-36x^2+4x-6$

$\displaystyle 48x^3-36x^2+4x-18$

Correct answer:

$\displaystyle 48x^3-36x^2+4x-6$

Explanation:

$\displaystyle 12x^4-3x^3+2x^2-12-6x-9x^3$

Simplify first:

$\displaystyle 12x^4-12x^3+2x^2-12-6x$

Use the power rule on each term:

Power rule: $x^a=ax^{a-1}$ $\displaystyle x^a=ax^{a-1}$

$\displaystyle 48x^3-36x^2+4x-6$

Note that constants become zero.

Report an Error

View Pre-Calculus Tutors

Chernyeh
Certified Tutor

Purdue University-Main Campus, Bachelor of Science, Business Administration and Management.

View Pre-Calculus Tutors

Jacob
Certified Tutor

Ohio State University-Main Campus, Bachelor of Science, Political Science and Government.

View Pre-Calculus Tutors

Muhammad
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Neuroscience.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Philadelphia, French Tutors in Los Angeles, ACT Tutors in Miami, Physics Tutors in New York City, Math Tutors in Los Angeles, SSAT Tutors in Washington DC, Physics Tutors in Chicago, SAT Tutors in Chicago, MCAT Tutors in Phoenix, GRE Tutors in New York City

Popular Courses & Classes

SAT Courses & Classes in Miami, ACT Courses & Classes in Denver, ACT Courses & Classes in Seattle, ISEE Courses & Classes in Philadelphia, SAT Courses & Classes in Seattle, ISEE Courses & Classes in Denver, SSAT Courses & Classes in Denver, MCAT Courses & Classes in Denver, Spanish Courses & Classes in Philadelphia, Spanish Courses & Classes in Denver

Popular Test Prep

SSAT Test Prep in Miami, ACT Test Prep in Denver, LSAT Test Prep in Chicago, GRE Test Prep in Chicago, SSAT Test Prep in Dallas Fort Worth, SSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Denver, LSAT Test Prep in Seattle, ACT Test Prep in Seattle, ISEE 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

Precalculus : Find the First Derivative of a Function

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #132 : Introductory Calculus

Example Question #41 : Find The First Derivative Of A Function

Example Question #41 : Find The First Derivative Of A Function

Example Question #758 : Pre Calculus

Example Question #759 : Pre Calculus

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: