To determine Calculate the value of d y d x at the point P ( 0 , 1 ) . Explanation Given information: The equation is 1 − x − y 2 − sin x y = 0 . The point is ( 0 , 1 ) . Theorem 8: A formula for implicit Differentiation : Let F ( x , y ) is differentiable and the equation F ( x , y ) = 0 defines y as a differentiable function of x . Then, at any point where F y ≠ 0 . d y d x = − F x F y Calculation: Show the equation as shown below: F ( x , y ) = 1 − x − y 2 − sin x y = 0 (1) Differentiate Equation (1) with respect to x . F x ( x , y ) = ∂ ∂ x ( 1 − x − y 2 − sin x y ) = − 1 − y cos x y Differentiate Equation (1) with respect to y . F y ( x , y ) = ∂ ∂ y ( 1 − x − y 2 − sin x y ) = − 2 y − x cos x y As per theorem, F ( x , y ) is differentiable and the equation F ( x , y ) = 0 defines y as a differentiable function of x

14th Edition

ISBN: 9780134654874

Author: WEIR

Publisher: VST

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Chapter 14, Problem 35PE

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Calculate the value of dydx at the point P(0,1).

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Chapter 14, Problem 34PE

Chapter 14, Problem 36PE

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