Problem 4. If h(x) = 5 ()+g(x)), where we know that f is one-to-one and f(2) = 3 f(3) = 4 f'(2) = -1 f'(3) = 11 g'(4) = -3, %3D %3D %3D g(2) = 4 g(4) = 3 g'(2) = 7 %3D then find h'(2) and (f-1)'(3).
Problem 4. If h(x) = 5 ()+g(x)), where we know that f is one-to-one and f(2) = 3 f(3) = 4 f'(2) = -1 f'(3) = 11 g'(4) = -3, %3D %3D %3D g(2) = 4 g(4) = 3 g'(2) = 7 %3D then find h'(2) and (f-1)'(3).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
only problem 4. I would like to compare my results.
![Problem 1. Calculate the derivatives of the following functions. Show all of your work and
clearly indicate any derivative rules that you use. Do not simplify your answers.
Let b denote the last nonzero digit of your UCID number, that is, if your UCID number
is 9876543210 then b = 1.
.2
(1) ƒ(x) = (2x + b)(e"¨+sin(ba))
%3D
(2) g(x) = tan-1(tan(bx)+sin-'(bx))
Note: tan-(x) = arctan(x) + e = cot(r).
1
tan(x)
|
(3) If g(x) is differentiable, find f'(x) where f(x) = g(x+b) cos-(x³).
%3D
Problem 2. In the following, use implicit differentiation.
dy
(1) If e – cos-y) = x, find
dx
dy
then find
d.x
(2) If x sec(y)
tan(x)'
dy
(3) If x + xy + y? = 3, then find the second derivative y"
%3D
dx?
Problem 3. Let b denote the last nonzero digit of your UCID number, that is, if your UCID
number is 9876543210 then b = 1.
If y = (x+ b)+b, find y'.
Problem 4. If h(x) = 5(f(x))²+g(x)], where we know that f is one-to-one and
%3D
f'(2) = -1
g'(2) = 7
f'(3) = 11
g'(4) = -3,
f(2) = 3
f(3) = 4
%3D
%3D
%3D
g(2) = 4
g(4) = 3
then find h'(2) and (f-1)'(3).
Problem 5. Consider the curve r = sin(y). Find the point on the curve where the tangent
%3D
line is parallel to the line y = -x and such that the y-coordinate of the point is (are) between
0< U< 2T) Thore may be one or more such points.
%3D
0.and 2r (i o](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d5280c1-0888-4121-94fb-2a368f5b3705%2F576a3b77-47a7-4a97-992a-db42ccd70940%2F9jemkl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1. Calculate the derivatives of the following functions. Show all of your work and
clearly indicate any derivative rules that you use. Do not simplify your answers.
Let b denote the last nonzero digit of your UCID number, that is, if your UCID number
is 9876543210 then b = 1.
.2
(1) ƒ(x) = (2x + b)(e"¨+sin(ba))
%3D
(2) g(x) = tan-1(tan(bx)+sin-'(bx))
Note: tan-(x) = arctan(x) + e = cot(r).
1
tan(x)
|
(3) If g(x) is differentiable, find f'(x) where f(x) = g(x+b) cos-(x³).
%3D
Problem 2. In the following, use implicit differentiation.
dy
(1) If e – cos-y) = x, find
dx
dy
then find
d.x
(2) If x sec(y)
tan(x)'
dy
(3) If x + xy + y? = 3, then find the second derivative y"
%3D
dx?
Problem 3. Let b denote the last nonzero digit of your UCID number, that is, if your UCID
number is 9876543210 then b = 1.
If y = (x+ b)+b, find y'.
Problem 4. If h(x) = 5(f(x))²+g(x)], where we know that f is one-to-one and
%3D
f'(2) = -1
g'(2) = 7
f'(3) = 11
g'(4) = -3,
f(2) = 3
f(3) = 4
%3D
%3D
%3D
g(2) = 4
g(4) = 3
then find h'(2) and (f-1)'(3).
Problem 5. Consider the curve r = sin(y). Find the point on the curve where the tangent
%3D
line is parallel to the line y = -x and such that the y-coordinate of the point is (are) between
0< U< 2T) Thore may be one or more such points.
%3D
0.and 2r (i o
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
We need to calculate h'(2) and (f^-1)'(3).
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning