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 given mathematical function is:
\[ f(x) = \sec^3(5x^4 - 18x^2) \]
This expression represents a function \( f(x) \) which is defined as the cube of the secant of a polynomial \( 5x^4 - 18x^2 \).
**Explanation:**
- \( \sec(x) \) is the secant function, which is the reciprocal of the cosine function, i.e., \( \sec(x) = \frac{1}{\cos(x)} \).
- The polynomial inside the secant function is \( 5x^4 - 18x^2 \).
- The entire expression \( \sec^3( \cdot ) \) indicates that the secant function is raised to the power of three.
This function might be used to illustrate concepts in advanced calculus, specifically those involving trigonometric transformations and polynomial functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe7817cb-5274-4434-90ec-13ab480c973d%2Ff0fcd929-97d2-40d6-9317-1e6ea7791fce%2Flmk8ujo_processed.png&w=3840&q=75)
Transcribed Image Text:The given mathematical function is:
\[ f(x) = \sec^3(5x^4 - 18x^2) \]
This expression represents a function \( f(x) \) which is defined as the cube of the secant of a polynomial \( 5x^4 - 18x^2 \).
**Explanation:**
- \( \sec(x) \) is the secant function, which is the reciprocal of the cosine function, i.e., \( \sec(x) = \frac{1}{\cos(x)} \).
- The polynomial inside the secant function is \( 5x^4 - 18x^2 \).
- The entire expression \( \sec^3( \cdot ) \) indicates that the secant function is raised to the power of three.
This function might be used to illustrate concepts in advanced calculus, specifically those involving trigonometric transformations and polynomial functions.
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