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

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 \(x\).
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The given function .
The aim is to find the derivative of the function.
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