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Calculate the derivative for the following function, but do not

Calculate the derivative for the following function, but do not

Calculus: Early Transcendentals
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

Calculate the derivative for the following function, but do not simplify.

The given function is: \[ f(x) = \sec^5(3x) \] This mathematical expression represents a trigonometric function where \( f(x) \) is the function of \( x \), and \( \sec \) denotes the secant function. The notation \( \sec^5(3x) \) indicates that the secant of \( 3x \) is raised to the fifth power. This type of function might be explored in an educational context where students learn about trigonometric identities, transformations, or calculus, particularly focusing on differentiation and integration of trigonometric functions.
Transcribed Image Text:The given function is: \[ f(x) = \sec^5(3x) \] This mathematical expression represents a trigonometric function where \( f(x) \) is the function of \( x \), and \( \sec \) denotes the secant function. The notation \( \sec^5(3x) \) indicates that the secant of \( 3x \) is raised to the fifth power. This type of function might be explored in an educational context where students learn about trigonometric identities, transformations, or calculus, particularly focusing on differentiation and integration of trigonometric functions.
The image presents a mathematical function written as: \[ f(x) = \sqrt{x + \sqrt{x}} \] This function is defined as the square root of the sum of a variable \( x \) and the square root of \( x \). The expression involves nested radicals, and the evaluation of this function requires calculating the innermost square root first, followed by the outer square root of the resulting sum. This type of function is often explored in algebra and calculus for understanding the behavior of nested functions and their domains. The domain of this function is constrained to non-negative values of \( x \) because square roots of negative numbers are not defined within the set of real numbers.
Transcribed Image Text:The image presents a mathematical function written as: \[ f(x) = \sqrt{x + \sqrt{x}} \] This function is defined as the square root of the sum of a variable \( x \) and the square root of \( x \). The expression involves nested radicals, and the evaluation of this function requires calculating the innermost square root first, followed by the outer square root of the resulting sum. This type of function is often explored in algebra and calculus for understanding the behavior of nested functions and their domains. The domain of this function is constrained to non-negative values of \( x \) because square roots of negative numbers are not defined within the set of real numbers.
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