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Consider the following equation. cos (y) = 27 Use implicit differentiation to determine an expression for y' as a function of and y. y'

Consider the following equation. cos (y) = 27 Use implicit differentiation to determine an expression for y' as a function of and y. y'

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
Consider the following equation. cos (y) = x7 Use implicit differentiation to determine an expression for y' as a function of and y. x y'
Transcribed Image Text:Consider the following equation. cos (y) = x7 Use implicit differentiation to determine an expression for y' as a function of and y. x y'
Expert Solution
Step 1: Formula of derivatives used:

Given equation, cos left parenthesis y right parenthesis equals x to the power of 7

We know,

left parenthesis i right parenthesis space fraction numerator d space over denominator d x end fraction left parenthesis x to the power of n right parenthesis equals n x to the power of n minus 1 end exponent left parenthesis i i right parenthesis space space fraction numerator d space over denominator d x end fraction left parenthesis cos x right parenthesis equals negative sin x

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