Explanation Given Information: The function is g ( x ) = ( sin x ) ( tan 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 ) = ( sin x ) ( tan x ) . Represent the function in the form of d y d x . d d x ( sin x ) ( tan x ) Then apply the product rule to the function d d x ( sin x ) ( tan x ) = ( tan x ) d d x ( sin x ) + ( sin x ) d d x ( tan x ) Further solve as, g ′ ( x ) = ( sin x cos x ) ⋅ ( cos x ) + ( sin x ) d d x ( sin x cos x ) Then apply the quotient rule to the function, g ′ ( x ) = ( sin x cos x ) ⋅ ( cos x ) + ( sin x ) d d x ( sin x cos x ) g ′ ( x ) = ( sin x ) + ( sin x

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

7th Edition

ISBN: 9781337291293

Author: Waner, Stefan; Costenoble, Steven

Publisher: Brooks Cole

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Chapter 9.2, Problem 3E

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Chapter 9.2, Problem 2E

Chapter 9.2, Problem 4E

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Chapter 9 Solutions

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

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The derivative of the function g ( x ) = ( sin x ) ( tan x ) .

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

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To calculate: The derivative of the function g(x)=(sinx)(tanx).

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Chapter 9 Solutions