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...
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Question 79, b
![Figure for 78
79. Proof Prove each differentiation formula.
d
-u'
(а)
dx
[arccos u] =
V1 – u²
d
u'
(b)
[arctan u]
dx
1 + u²
d
u'
(c)
[arcsec u]
dx
|u| /u²
d
(d)
[arccot u]
%3|
dx
1 + u²
d
- u'
(e)
[arccsc u]
dx
80. Existence of an Inverse Determine the values of k sucl
that the function f(x) = kx + sin x has an inverse function.
%D
True or False?
statement is true or false. If it is false, explain why or give an
example that shows it is false.
In Exercises 81-84, determine whether the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39660209-0130-4531-8e39-edad714133c0%2F32c50198-7ce7-4d3e-b4d4-390c675482c8%2Flp4pfjq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Figure for 78
79. Proof Prove each differentiation formula.
d
-u'
(а)
dx
[arccos u] =
V1 – u²
d
u'
(b)
[arctan u]
dx
1 + u²
d
u'
(c)
[arcsec u]
dx
|u| /u²
d
(d)
[arccot u]
%3|
dx
1 + u²
d
- u'
(e)
[arccsc u]
dx
80. Existence of an Inverse Determine the values of k sucl
that the function f(x) = kx + sin x has an inverse function.
%D
True or False?
statement is true or false. If it is false, explain why or give an
example that shows it is false.
In Exercises 81-84, determine whether the
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