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f(w) = cos (sin ¹2w) -

f(w) = cos (sin ¹2w) -

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
Evaluate the derivative
**Problem 15:** Given the function \( f(w) = \cos(\sin^{-1}(2w)) \). This mathematical expression involves the use of trigonometric functions: 1. \(\sin^{-1}(2w)\) refers to the inverse sine (also known as arcsine) of \(2w\). 2. \(\cos(\cdot)\) then applies the cosine function to the result of the inverse sine. Understanding this equation requires a grasp of inverse trigonometric functions and their properties, particularly how the angle output of \(\sin^{-1}\) works as an input for the cosine function. Note that \(-1 \leq \sin^{-1}(x) \leq 1\) for the domain of \(x\). There are no graphs or diagrams in this image.
Transcribed Image Text:**Problem 15:** Given the function \( f(w) = \cos(\sin^{-1}(2w)) \). This mathematical expression involves the use of trigonometric functions: 1. \(\sin^{-1}(2w)\) refers to the inverse sine (also known as arcsine) of \(2w\). 2. \(\cos(\cdot)\) then applies the cosine function to the result of the inverse sine. Understanding this equation requires a grasp of inverse trigonometric functions and their properties, particularly how the angle output of \(\sin^{-1}\) works as an input for the cosine function. Note that \(-1 \leq \sin^{-1}(x) \leq 1\) for the domain of \(x\). There are no graphs or diagrams in this image.
Expert Solution
Step 1: Given the information

The given function f open parentheses w close parentheses equals cos open parentheses sin to the power of negative 1 end exponent open parentheses 2 w close parentheses close parentheses.

The aim is to find the derivative of the function.

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