(a) Explanation In implicit differentiation method, differentiate both the sides of the given equation with respect to x such that the derivative of any term that contains y includes the factor d y d x . Next solve the resulting equation for d y d x in terms of x and y . Consider an example, Assume the function is F ( x , y ) = y 4 − y + 3 x 3 − x = 8 . Differentiate both the sides in the given equation with respect to x , d d x ( y 4 − y + 3 x 3 − x ) = d d x ( 8 ) d d x ( y 4 ) − d d x ( (b) To determine To explain: The role of the Chain Rule in implicit differentiation.

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 3.6, Problem 1CQ

(a)

To determine

To explain: The role of implicit differentiation to find the solution of dydx .

(b)

To determine

To explain: The role of the Chain Rule in implicit differentiation.

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Chapter 3.5, Problem 8TE

Chapter 3.6, Problem 2CQ

Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ 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 Ch. 3.1 - Prob. 6E

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Volume of a Cylinder The volume of a...Ch. 3.6 - Prob. 40E Ch. 3.6 - Prob. 41E Ch. 3.6 - Prob. 42E Ch. 3.6 - Prob. 43E Ch. 3.6 - Prob. 44E Ch. 3.6 - Prob. 45E Ch. 3.6 - Prob. 46E Ch. 3.6 - Prob. 47E Ch. 3.6 - PRODUCTION FUNCTION FOR A FURNITURE COMPANY The...Ch. 3.6 - Prob. 49E Ch. 3.6 - Prob. 50E Ch. 3.6 - Prob. 51E Ch. 3.6 - Prob. 52E Ch. 3.6 - Prob. 53E Ch. 3.6 - Prob. 54E Ch. 3.6 - Prob. 55E Ch. 3.6 - Prob. 56E Ch. 3.6 - Prob. 57E Ch. 3.6 - Prob. 58E Ch. 3.6 - Prob. 59E Ch. 3.6 - Prob. 60E Ch. 3.6 - Prob. 61E Ch. 3.6 - Prob. 62E Ch. 3.6 - Prob. 63E Ch. 3.6 - Prob. 64E Ch. 3.6 - Prob. 65E Ch. 3.6 - 66. 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The role of implicit differentiation to find the solution of d y d x .

Solution Summary: The author explains the role of the chain rule in implicit differentiation, which is used in differentiation of a term containing y.

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To explain: The role of implicit differentiation to find the solution of dydx .

To explain: The role of the Chain Rule in implicit differentiation.

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Chapter 3 Solutions