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 #281 : Derivative Review

Find the derivative of f(x)=4x^2-5x+3 .

Possible Answers:

$f{}'(x)=8x-\frac{5}{x}$

f{}'(x)=8x

$f{}'(x)=8x^2$

f{}'(x)=8x-5

f'(x)=0

Correct answer:

f{}'(x)=8x-5

Explanation:

Recall that when taking the derivative, multiply the exponent of the x term by the coefficient in front and then subtract one from the exponent.

Therefore, your answer is

f{}'(x)=8x-5 .

Report an Error

Example Question #282 : Derivatives

Find the derivative of x^2+y^2=1 .

Possible Answers:

$\frac{dy}{dx}=-\frac{2x}{y}$

$\frac{dy}{dx}=\frac{x}{y}$

$\frac{dy}{dx}=-\frac{x}{2y}$

$\frac{dy}{dx}=-\frac{x}{y}$

$\frac{dy}{dx}=1$

Correct answer:

$\frac{dy}{dx}=-\frac{x}{y}$

Explanation:

To find the derivative here, you have to use implicit differentiation.

The first step is to take the derivative of each term using the power rule,

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

in this particular case it would look like this:

$2x+2y\frac{dy}{dx}=0$ .

Then, solve for $\frac{dy}{dx}$ .

Therefore, your answer is:

$\frac{dy}{dx}=-\frac{x}{y}$ .

Report an Error

Example Question #282 : Derivatives

Find the first derivative of f(x)=4x^2+2x+1

Possible Answers:

None of the Above

-8x+2

8x-2

8x+2

Correct answer:

8x+2

Explanation:

Step 1: Recall the derivative rules:

-For any term with an exponent, the exponent drops and gets multiplied to the coefficient of that term. The new exponent is one less than the original one..
-For any term in the form "ax", the derivative of this term is just the coefficient.
-For any term with no x term (constant), the derivative is always

Step 2: Take the derivative:

$f'(x)=(4\cdot 2)x^{2-1}+2(1)+0=8x+2$

The first derivative of f(x) is 8x+2

Report an Error

Example Question #282 : Derivative Review

Find the first derivative of $f(x)=\frac {1}{x^3}$

Possible Answers:

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

$-\frac {3}{x^2}$

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

$\frac {3}{x^3}$

Correct answer:

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

Explanation:

Step 1: Re-write the function in terms of a term, not a fraction:

$\frac {1}{x^3}=x^{-3}$

Step 2: Using the power rule, the drops down and is put in front of the x term. The exponent gets subtracted by , which means -3-1=-4 . is the new exponent..

$-3x^{-4}$

Step 3: Re-write the exponents with positive numbers...

When we change the exponents to positive from negative, you flip the exponent term over . We can rewrite $x^{-4}$ as $\frac {1}{x^4}$ .

Step 4: Multiply the coefficient from Step and the fraction in step to get the derivative:

$-3 \cdot \frac {1}{x^4}=-\frac {3}{x^4}$

Report an Error

Example Question #282 : Derivative Review

Find the derivative of $3^{x^2}$ .

Possible Answers:

$2x3^{x^2}ln(3)$

$6^{x^2}ln(3)$

$3^{2x}ln(3)$

$6^{2x}ln(3)$

$3^{x^2}ln(3)$

Correct answer:

$2x3^{x^2}ln(3)$

Explanation:

This is a special derivative.

$\frac{d}{dx}a^u=a^ulna\frac{du}{dx}.$

$\frac{d}{dx}3^{x^2}=3^{x^2}*ln3*\frac{d(x^2)}{dx}=3^{x^2}ln3*2x.$

Report an Error

Example Question #283 : Derivatives

What is the derivative of the following function?

$f(x)=10^{sinx}$ .

Possible Answers:

$10^{cosx}*ln(10)$

$10^{sinx}*ln(10)*cos(x)$

$10^{sinx}*ln(10)*x$

$10^{sinx}*ln(sinx)$

$10^{sinx}*ln(10)$

Correct answer:

$10^{sinx}*ln(10)*cos(x)$

Explanation:

The derivative of a constant raised to a power is given by the following equation.

$\frac{d}{dx}a^u=a^ulna\frac{du}{dx}$

$\frac{d}{dx}10^{sinx}=10^{sinx}ln(10)\frac{d(sinx)}{dx}=10^{sinx}*ln(10)*cosx.$

Report an Error

Example Question #285 : Derivatives

Find the derivative of $f(x)=3x^{2/3}+8x^{-1/2}$

Possible Answers:

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

$f'(x)=2x^{-1/3}-4x^{1/2}$

$f'(x)=2x^{-1/3}+4x^{1/2}$

$f'(x)=2x^{-1/3}-4x^{-3/2}$

$f'(x)=2x^{-1/3}-8x^{-3/2}$

Correct answer:

$f'(x)=2x^{-1/3}-4x^{-3/2}$

Explanation:

This derivative is an application of the power rule. Remember, we need to multiply the coefficient by the exponent, then reduce the exponent by one.

$f(x)=3x^{2/3}+8x^{-1/2}$

$f'(x)=3*\frac{2}{3}x^{2/3-1}+8*\frac{-1}{2}x^{-1/2-1}=2x^{-1/3}-4x^{-3/2}.$

Report an Error

Example Question #284 : Derivatives

Find the derivative of the function:

$f(x)=\cos(e^{5x})$

Possible Answers:

$-5e^{4x}\sin(e^{5x})$

$-5e^{5x}\sin(e^{5x})$

$5e^{5x}\sin(e^{5x})$

$-e^{5x}\sin(e^{5x})$

Correct answer:

$-5e^{5x}\sin(e^{5x})$

Explanation:

The derivative of the function is equal to

$f'(x)=-5e^{5x}\sin(e^{5x})$

and was found using the following rules:

$\frac{\mathrm{d} }{\mathrm{d} x} f(g(x))=f'(g(x))\cdot g'(x)$ , $\frac{\mathrm{d} }{\mathrm{d} x} \cos(x)=-\sin(x)$ , $\frac{\mathrm{d} }{\mathrm{d} x} e^u=e^u\frac{\mathrm{du} }{\mathrm{d} x}$ , $\frac{\mathrm{d} }{\mathrm{d} x} x^n=nx^{n-1}$

Report an Error

Example Question #289 : Derivatives

Find the derivative of the function:

$f(x)=\sec(x^2+x+10)$

Possible Answers:

$\sec(x^2+x+10)\tan(x^2+x+10)$

$(2x+1)\sec(x^2+x+10)\tan(x^2+x+10)$

$(2x+1)\ln\left |\sec(x^2+x+10)+\tan(x^2+x+10) \right |$

$-(2x+1)\sec(x^2+x+10)\tan(x^2+x+10)$

Correct answer:

$(2x+1)\sec(x^2+x+10)\tan(x^2+x+10)$

Explanation:

The derivative of the function is equal to

$f'(x)=(2x+1)\sec(x^2+x+10)\tan(x^2+x+10)$

and was found using the following rules:

$\frac{\mathrm{d} }{\mathrm{d} x} f(g(x))=f'(g(x))\cdot g'(x)$ , $\frac{\mathrm{d} }{\mathrm{d} x} \sec(x)=\sec(x)\tan(x)$ , $\frac{\mathrm{d} }{\mathrm{d} x} x^n=nx^{n-1}$

Report an Error

Example Question #283 : Derivatives

Find the derivative of the function:

$f(x)=\frac{x}{e^x}$

Possible Answers:

$\frac{1+x}{e^x}$

$\frac{1-x}{e^{x^2}}$

$\frac{1-x}{e^x}$

$\frac{1}{e^x}$

Correct answer:

$\frac{1-x}{e^x}$

Explanation:

The derivative of the function is equal to

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

and was found using the following rules:

$\frac{\mathrm{d} }{\mathrm{d} x} \frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{g(x)^2}$ , $\frac{\mathrm{d} }{\mathrm{d} x} e^x=e^x$ , $\frac{\mathrm{d} }{\mathrm{d} x} x^n=nx^{n-1}$

Report an Error

View Calculus 2 Tutors

Tahir
Certified Tutor

Cleveland State University, Master of Science, Electrical Engineering.

View Calculus 2 Tutors

Amanda
Certified Tutor

College of William and Mary, Bachelor in Arts, Anthropology.

View Calculus 2 Tutors

Ahmed
Certified Tutor

Toronto Metropolitan University, Bachelor, Computer Engineering.

All Calculus 2 Resources

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

Popular Subjects

Computer Science Tutors in Houston, LSAT Tutors in San Francisco-Bay Area, French Tutors in Boston, Reading Tutors in Houston, ISEE Tutors in Washington DC, GMAT Tutors in San Diego, Algebra Tutors in Seattle, Biology Tutors in Boston, GMAT Tutors in Dallas Fort Worth, SSAT Tutors in Atlanta

Popular Courses & Classes

SAT Courses & Classes in Miami, ISEE Courses & Classes in Seattle, GRE Courses & Classes in Denver, SSAT Courses & Classes in Denver, MCAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Atlanta, MCAT Courses & Classes in Washington DC, GRE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in San Diego

Popular Test Prep

LSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Philadelphia, GRE Test Prep in Houston, LSAT Test Prep in Houston, SSAT Test Prep in Miami, GMAT Test Prep in Houston, GRE Test Prep in San Francisco-Bay Area, SAT Test Prep in Phoenix, SAT 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 2 : Derivative Review

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #281 : Derivative Review

Example Question #282 : Derivatives

Example Question #282 : Derivatives

Example Question #282 : Derivative Review

Example Question #282 : Derivative Review

Example Question #283 : Derivatives

Example Question #285 : Derivatives

Example Question #284 : Derivatives

Example Question #289 : Derivatives

Example Question #283 : Derivatives

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: