(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.

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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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

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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 .

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Chapter 3 Solutions