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y = CSC ²³ ( 5x ³ + 2) 3

y = CSC ²³ ( 5x ³ + 2) 3

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
Find dy/dx and simplify if possible:
The given mathematical expression is: \[ y = \csc^3(5x^3 + 2) \] This is a trigonometric function where \( \csc \) denotes the cosecant, which is the reciprocal of the sine function, expressed as \( \csc(x) = \frac{1}{\sin(x)} \). ### Explanation: - **Function Composition:** The expression inside the cosecant function is \( 5x^3 + 2 \). This represents a polynomial function used as the argument for the cosecant. - **Cosecant Cubed:** The entire cosecant term is raised to the third power, meaning you take the cosecant of the polynomial and cube the result. This expression might be used to explore the properties of trigonometric functions in a calculus context, such as finding derivatives or integrals. Depending on the course, it might be part of a lesson on chain rule differentiation or trigonometric identities.
Transcribed Image Text:The given mathematical expression is: \[ y = \csc^3(5x^3 + 2) \] This is a trigonometric function where \( \csc \) denotes the cosecant, which is the reciprocal of the sine function, expressed as \( \csc(x) = \frac{1}{\sin(x)} \). ### Explanation: - **Function Composition:** The expression inside the cosecant function is \( 5x^3 + 2 \). This represents a polynomial function used as the argument for the cosecant. - **Cosecant Cubed:** The entire cosecant term is raised to the third power, meaning you take the cosecant of the polynomial and cube the result. This expression might be used to explore the properties of trigonometric functions in a calculus context, such as finding derivatives or integrals. Depending on the course, it might be part of a lesson on chain rule differentiation or trigonometric identities.
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