Explanation Given Information: The function is g ( x ) = ( cos x ) ( cot x ) . Formula Used: The product rule is used which can be represented as follows: d d x ( x ⋅ y ) = d d x ( x ) ⋅ y + x ⋅ d y d x The quotient rule is used which can be represented as follows: d d x ( x y ) = d d x ( x ) ⋅ y − x ⋅ d y d x y 2 The following derivative formulas are used: d d x ( sin x ) = cos x d d x ( cos x ) = − sin x Calculation: Consider the function g ( x ) = ( cos x ) ( cot x ) . Represent the function in the form of d y d x . d d x ( cos x ) ( cot x ) Then apply the product rule to the function d d x ( cos x ) ( cot x ) = ( cot x ) ⋅ d d x ( cos x ) + ( cos x ) d d x ( cot x ) Further solve as, g ′ ( x ) = ( cot x ) ⋅ ( − sin x ) + ( cos x ) d d x ( cos x sin x ) Then apply the quotient rule to the function g ′ ( x ) = ( cot x ) ⋅ ( − sin x ) + ( cos x ) d d x ( cos x sin x ) = ( cot x ) ⋅ ( − sin x ) + ( cos x ) ( sin x ) ⋅ d d x ( cos x ) − ( cos x ) ⋅ d d x ( s

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Chapter 16.2, Problem 4E

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To calculate: The derivative of the function g(x)=(cosx)(cotx).

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Chapter 16.2, Problem 3E

Chapter 16.2, Problem 5E

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Chapter 16 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

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The derivative of the function g ( x ) = ( cos x ) ( cot x ) .

Solution Summary: The author explains how to calculate the derivative of the function g(x)= (mathrmcos

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Chapter 16 Solutions