(a) Explanation Given information : The function cos x + y = 5 . Formula used: Power Rule for differentiation, d d x ( x n ) = n x n − 1 . Calculation : Consider the function cos x + y = 5 . Differentiate both sides with respect to x , d d x ( cos x + y ) = d d x ( 5 ) d d x ( cos x + y 1 2 ) = d d x ( 5 ) Since y is a function of x , apply the Power Rule for differentiation for the term y 1 2 Recall the Power Rule for differentiation, d d x ( x n ) = n x n − 1 (b) To determine To calculate : The equation cos x + y = 5 explicitly for y and differentiate to obtain y ' in terms of x . (c) To determine To verify : The solutions obtained in part (a) and (b) are consistent by substituting the expression for y into solution of part (a).

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ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3.5, Problem 64E

(a)

To determine

To calculate: The value of y' for the function cosx+y=5 with help of implicit differentiation.

(b)

To determine

To calculate: The equation cosx+y=5 explicitly for y and differentiate to obtain y' in terms of x .

(c)

To determine

To verify: The solutions obtained in part (a) and (b) are consistent by substituting the expression for y into solution of part (a).

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Chapter 3.5, Problem 63E

Chapter 3.5, Problem 65E

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The value of y ' for the function cos x + y = 5 with help of implicit differentiation .

Solution Summary: The author analyzes the function mathrmcosx+sqrty=5 with implicit differentiation.

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To calculate: The value of y' for the function cosx+y=5 with help of implicit differentiation.

To calculate: The equation cosx+y=5 explicitly for y and differentiate to obtain y' in terms of x .

To verify: The solutions obtained in part (a) and (b) are consistent by substituting the expression for y into solution of part (a).

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