Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Math 251 Quiz: Derivatives and Inverse Functions, Quizzes of Calculus

University of Oregon (UO)Calculus

Material Type: Quiz; Class: Calculus I >4; Subject: Mathematics; University: University of Oregon; Term: Fall 2006;

Typology: Quizzes

Pre 2010

Uploaded on 07/23/2009

koofers-user-9sk
koofers-user-9sk 🇺🇸

10 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Quiz for Math 251 (CRN 15056), Week 7
Note: Show your work! These are the important basis for grading.
Name
1. True or false. (25 points)
a) If g(x) = f−1(x), then g0(x) = 1
f0(x). T F
b) (tan x)0=1
1 + tan2x. T F
c) (tan−1x)0=1
1 + tan2x. T F
d) d4
dx4sin x= sin x. T F
e) d2
dx2(f·g) = ( d2
dx2f)·g+f·(d2
dx2g), here fand gare abbreviations for
functions f(x) and g(x).
T F
2. Find the derivative of y=(x+ 1)2·(x−2)
3√x−1·x3. (25 points)
1
pf2

Partial preview of the text

Download Math 251 Quiz: Derivatives and Inverse Functions and more Quizzes Calculus in PDF only on Docsity!

Quiz for Math 251 (CRN 15056), Week 7

Note: Show your work! These are the important basis for grading.

Name

  1. True or false. (25 points)

a) If g(x) = f −^1 (x), then g′(x) =

f ′(x)

. T F

b) (tan x)′^ =

1 + tan^2 x

. T F

c) (tan−^1 x)′^ =

1 + tan^2 x

. T F

d)

d^4 dx^4 sin x = sin x. T F

e) d^2 dx^2

(f · g) = ( d^2 dx^2

f ) · g + f · ( d^2 dx^2

g), here f and g are abbreviations for functions f (x) and g(x).

T F

  1. Find the derivative of y =

(x + 1)^2 · (x − 2) 3

x − 1 · x^3

. (25 points)

  1. f (x) = sin sin x for − 1 ≤ x ≤ 1. On the domain (− 1 , 1), f (x) is a one-to-one function, thus we may define f −^1 (x), just let g(x) = f −^1 (x). As sin(sin 0) = 0, it is obvious that g(0) = f −^1 (0) = 0. The question: Find the value of g′(0). (i.e, find the derivative of inverse function of f at 0) (25 points).
  2. Use implicit differentiation to find y′^ at (0, 0) for

x · sin y + (x + 1)^2 · ey^ = 1

(25 points)