Explanation Given: x and y are functions of a variable t and use implicit differentiation to relate d y d t and d x d t . x . y = 1 Calculation: Using product rule, and differentiate both site w.r.t. ‘t’ d d t ( x . y ) = d d t ( 1 ) = x . d y d t + − y . d x d t = 0 ⇒ x ...

Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover

3rd Edition

ISBN: 9781319048518

Author: Colin Adams Jon Rogawski

Publisher: Macmillan Higher Education

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Question

Chapter 3.8, Problem 81E

To determine

To derive:

The relation $\frac{d y}{d t} = - \frac{y}{x} \frac{d x}{d t}$ by differentiating $x y = 1$ with respect to t.

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Chapter 3.8, Problem 80E

Chapter 3.8, Problem 82E

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Chapter 3 Solutions

Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover

Ch. 3.1 - Prob. 1PQ Ch. 3.1 - Prob. 2PQ Ch. 3.1 - Prob. 3PQ Ch. 3.1 - Prob. 4PQ Ch. 3.1 - Prob. 5PQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E

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To derive: The relation d y d t = − y x d x d t by differentiating x y = 1 with respect to t.

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To derive: The relation dydt=−yxdxdt by differentiating xy=1with respect to t.

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To derive:

The relation $\frac{d y}{d t} = - \frac{y}{x} \frac{d x}{d t}$ by differentiating $x y = 1$ with respect to t.