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
Find f prime of x
![The image shows a mathematical function, specifically:
\[ f(x) = 2 \tan(\cos x) \]
Where:
- \( f(x) \) represents the function of \( x \).
- \( \tan \) denotes the tangent function, which is a trigonometric function.
- \( \cos \) denotes the cosine function, which is also a trigonometric function.
This function \( f(x) \) can be interpreted as follows:
1. First, the cosine of \( x \) is calculated.
2. Then, the tangent of the result from the cosine function is computed.
3. Finally, this value is multiplied by 2 to obtain the value of \( f(x) \).
Understanding the composition of trigonometric functions is crucial for analyzing their behaviors and properties. When graphing this function, one should keep in mind how the cosine function, which oscillates between -1 and 1, affects the input to the tangent function, which has vertical asymptotes and undefined values for certain inputs. This composition will result in a complex graph with periodic behaviors and discontinuities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe7817cb-5274-4434-90ec-13ab480c973d%2Fd2448bbc-1109-4589-b3aa-ebfda56c4540%2Fufm9nd_processed.png&w=3840&q=75)
Transcribed Image Text:The image shows a mathematical function, specifically:
\[ f(x) = 2 \tan(\cos x) \]
Where:
- \( f(x) \) represents the function of \( x \).
- \( \tan \) denotes the tangent function, which is a trigonometric function.
- \( \cos \) denotes the cosine function, which is also a trigonometric function.
This function \( f(x) \) can be interpreted as follows:
1. First, the cosine of \( x \) is calculated.
2. Then, the tangent of the result from the cosine function is computed.
3. Finally, this value is multiplied by 2 to obtain the value of \( f(x) \).
Understanding the composition of trigonometric functions is crucial for analyzing their behaviors and properties. When graphing this function, one should keep in mind how the cosine function, which oscillates between -1 and 1, affects the input to the tangent function, which has vertical asymptotes and undefined values for certain inputs. This composition will result in a complex graph with periodic behaviors and discontinuities.
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