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Differentiate: x¹0 cos(x)

Differentiate: x¹0 cos(x)

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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**Differentiate:** \( x^{10} \cos(x) \) Options: A) \( 10x^9 - \sin(x) \) B) \(-10x^9 \sin(x)\) C) \(-x^{10} \cos(x) + 10x^9 \sin(x)\) D) \(10x - \sin(x)\) E) \(-10x \sin(x)\) F) \(-x^{10} \sin(x) + 10x^9 \cos(x)\) The problem asks for the derivative of the function \( x^{10} \cos(x) \). Consider applying the product rule for differentiation since the expression is a product of two functions, \( x^{10} \) and \( \cos(x) \). The product rule states: \( (uv)' = u'v + uv' \). Choose the correct option based on these calculations.
Transcribed Image Text:**Differentiate:** \( x^{10} \cos(x) \) Options: A) \( 10x^9 - \sin(x) \) B) \(-10x^9 \sin(x)\) C) \(-x^{10} \cos(x) + 10x^9 \sin(x)\) D) \(10x - \sin(x)\) E) \(-10x \sin(x)\) F) \(-x^{10} \sin(x) + 10x^9 \cos(x)\) The problem asks for the derivative of the function \( x^{10} \cos(x) \). Consider applying the product rule for differentiation since the expression is a product of two functions, \( x^{10} \) and \( \cos(x) \). The product rule states: \( (uv)' = u'v + uv' \). Choose the correct option based on these calculations.
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