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If 4xy = x² + y², use implicit differentiation to find y" (that is, the second derivative of y with respect to x). Show your work.

If 4xy = x² + y², use implicit differentiation to find y" (that is, the second derivative of y with respect to x). Show your work.

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
If 4xy = x2 + y², use implicit differentiation to find y" (that is, the second derivative of y with respect to x). Show your work.
Transcribed Image Text:If 4xy = x2 + y², use implicit differentiation to find y" (that is, the second derivative of y with respect to x). Show your work.
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.

\large 4xy=x^2+y^2

take derivative

\large \frac{d}{dx}\left(4xy\right)=\frac{d}{dx}\left(x^2+y^2\right)

\large 4\left(\frac{d}{dx}\left(x\right)y+\frac{d}{dx}\left(y\right)x\right)=\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(y^2\right)

\large 4\left(y+y'x\right)=2x+2y\cdot y'

\large 4y+4xy'=2x+2y\cdot y'

\large 4y+4xy'-2x-2y\cdot y'=0

divide both sides by 2

\large 2y+2xy'-x-y\cdot y'=0.................(1)

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