Explanation Given: The given equation is x y 2 + x 2 y = 2 at ( 1 , 1 ) . Concept Used: Product rule of differentiation formula d d x ( u v ) = v d d x u + u d d x v Chain rule of differentiation is: d d x f [ g ( x ) ] = d d g f ( g ) d g d x , where u is a differentiable function at x and f is a differentiable function at u ( x ) To find an equation of the tangent line to the graph of an equation y = f ( x ) at the a point ( a , b ) First find slope of the equation at the prescribed point as: m = d y d x | ( a , b ) Now, the equation of the tangent line to the graph of the equation is y = m x + c Put ( a , b ) coordinate in y = m x + c to find the value of c Calculation: To find an equation of the tangent line to the graph of x y 2 + x 2 y = 2 at ( 1 , 1 ) First find slope of the equation at the prescribed point as: m = d y d x | ( a , b ) For that differentiate both side of the equation with respect to x as x y 2 + x 2 y = 2 d d x ( x y 2 + x 2 y ) = d d x 2 d d x ( x y 2 ) + d d x ( x 2 y ) = 0 x d d x y 2 + y 2

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3, Problem 41SP

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To find an equation of the tangent line to the graph of given equation xy2+x2y=2 at (1,1) .

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Chapter 3, Problem 40SP

Chapter 3, Problem 42SP

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Chapter 3 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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To find an equation of the tangent line to the graph of given equation x y 2 + x 2 y = 2 at ( 1 , 1 ) .

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To find an equation of the tangent line to the graph of given equation xy2+x2y=2 at (1,1) .

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Chapter 3 Solutions