We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Create an account to track your scores
and create your own practice tests:

Create an Account Create a Practice Test

All Calculus AB Resources

45 Practice Tests Question of the Day Flashcards Learn by Concept

Want to review Calculus AB but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different Calculus AB flashcards! Our Calculus AB flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous Calculus AB flashcards.

Flashcards: Determine Local Linearity and Linearization

Differentiate,

$y = \sin(\sin(\sin\(3x)))$

$\frac{dy}{dx}=3\cos(\cos(\sin(3x)))\times \sin(\sin(3x))\times \sin(3x)$

$\frac{dy}{dx}=3\cos(\sin(\sin(3x)))\times \cos(\sin(3x))$

$\frac{dy}{dx}=3\cos(\cos(\sin(3x)))\times \cos(\sin(3x))$

$\frac{dy}{dx}=3\cos(\sin(\sin(x)))\times \sin(\sin(x))\times \cos(3x)$

$\frac{dy}{dx}=3\cos(\sin(\sin(3x)))\times \cos(\sin(3x))\times \cos(3x)$

Report an Error Copyright Notice

Flashcards: Determine Local Linearity and Linearization

Differentiate,

$y = \sin(\sin(\sin\(3x)))$

Your answer:

$\frac{dy}{dx}=3\cos(\cos(\sin(3x)))\times \sin(\sin(3x))\times \sin(3x)$

Your answer:

$\frac{dy}{dx}=3\cos(\sin(\sin(3x)))\times \cos(\sin(3x))$

Your answer:

$\frac{dy}{dx}=3\cos(\cos(\sin(3x)))\times \cos(\sin(3x))$

Your answer:

$\frac{dy}{dx}=3\cos(\sin(\sin(x)))\times \sin(\sin(x))\times \cos(3x)$

Correct answer:

$\frac{dy}{dx}=3\cos(\sin(\sin(3x)))\times \cos(\sin(3x))\times \cos(3x)$

Explanation:

Differentiate,

$y = \sin(\sin(\sin\(3x)))$

Strategy

This one at first glance appears difficult even if we recognize that the chain rule is needed; we have a function within a function within a function within a function. To avoid making mistakes, it's best to start by defining variables to make the calculation easier to follow.

Let's start with the outermost function, we will write as a function of by setting,

$u = \sin(\sin(3x))$

______________________________________________________

$y = \sin(\underset{u}{ \underbrace{\sin(\sin(3x))}}) = \sin(u)$

$y = \sin(u)$

_______________________________________________________

Similarly, define to write as a function of

$u = \sin(\underset{v}{ \underbrace{\sin(3x)}}) = \sin(v)$

$u = \sin(v)$

_______________________________________________________

Write as a function of

$v = \sin(\underset{w}{ \underbrace{3x}} )=\sin(w)$

$v = \sin(w)$

_______________________________________________________

Finally, define the inner-most function, , as the function of

w=3x

________________________________________________________

$\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dv}\frac{dv}{dw}\frac{dw}{dx}$

Since $\frac{dw}{dx}=3$ we will just substitute that in and move to the front.

$\frac{dy}{dx}=3\cos(u)\cos(v)\cos(w)$

That was easy enough, now just write everything in terms of by going back to the definitions of and .

$u = \sin(\sin(3x))$

$v = \sin(3x)$

w = 3x

$\frac{dy}{dx}=3\cos(\sin(\sin(3x)))\times \cos(\sin(3x))\times \cos(3x)$

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)

View Tutors

Darlene
Certified Tutor

Drake University, Bachelor of Science, Elementary School Teaching. Drake University, Masters in Education, Education.

View Tutors

Anastasiia
Certified Tutor

KPI (Kyiv Polytechnic Institute), Bachelor, Journalism.

View Tutors

Artik
Certified Tutor

Campbell University, Master of Science, Pharmaceutical Sciences.

Popular Subjects

MCAT Tutors in Phoenix, Chemistry Tutors in San Francisco-Bay Area, Calculus Tutors in Boston, Statistics Tutors in New York City, English Tutors in Atlanta, Computer Science Tutors in San Francisco-Bay Area, English Tutors in New York City, Reading Tutors in Chicago, SAT Tutors in Boston, Computer Science Tutors in Phoenix

Popular Courses & Classes

SSAT Courses & Classes in Washington DC, MCAT Courses & Classes in Boston, SAT Courses & Classes in Washington DC, GRE Courses & Classes in Miami, MCAT Courses & Classes in Seattle, ACT Courses & Classes in New York City, Spanish Courses & Classes in Atlanta, ISEE Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Los Angeles, GRE Courses & Classes in Washington DC

Popular Test Prep

GMAT Test Prep in Boston, GMAT Test Prep in Los Angeles, SAT Test Prep in Los Angeles, SAT Test Prep in Houston, MCAT Test Prep in Chicago, ACT Test Prep in Dallas Fort Worth, GMAT Test Prep in Seattle, ISEE Test Prep in Phoenix, MCAT Test Prep in Houston, GMAT Test Prep in Phoenix

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores
and create your own practice tests:

All Calculus AB Resources

Flashcards: Determine Local Linearity and Linearization

Flashcards: Determine Local Linearity and Linearization

Flashcards: Determine Local Linearity and Linearization

Flashcards: Determine Local Linearity and Linearization

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback:

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores and create your own practice tests:

All Calculus AB Resources

Flashcards: Determine Local Linearity and Linearization

Flashcards: Determine Local Linearity and Linearization

Flashcards: Determine Local Linearity and Linearization

Flashcards: Determine Local Linearity and Linearization

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Create an account to track your scores
and create your own practice tests: