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3. Let x² + 4xy + y² = 13. dy • Find dx by using implicit differentiation.

3. Let x² + 4xy + y² = 13. dy • Find dx by using implicit differentiation.

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
### Mathematics Exercises on Implicit Differentiation 3. Given the equation \(x^2 + 4xy + y^2 = 13\): - **Task 1**: Find \(\frac{dy}{dx}\) using implicit differentiation. - **Task 2**: Write an equation of the tangent line to the curve at the point \((2, 1)\). 4. Given the equation \(\sin^2 x + \cos^2 y = x^2 + y^2\): - Find \(y'\) by using implicit differentiation.
Transcribed Image Text:### Mathematics Exercises on Implicit Differentiation 3. Given the equation \(x^2 + 4xy + y^2 = 13\): - **Task 1**: Find \(\frac{dy}{dx}\) using implicit differentiation. - **Task 2**: Write an equation of the tangent line to the curve at the point \((2, 1)\). 4. Given the equation \(\sin^2 x + \cos^2 y = x^2 + y^2\): - Find \(y'\) by using implicit differentiation.
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x^2+xy+y^2=13

take derivative on both sides

\frac{d}{dx}\left(x^2+xy+y^2\right)=\frac{d}{dx}\left(13\right)

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