Explanation Given Information: The function is y ( x ) = cos ( e x ) + e x cos x . Formula Used: The chain rule is used which can be represented with the following formula: d d x ( cos u ) = d d x ( cos u ) ⋅ d u d x The product rule is used which can be represented with the following formula: d d x ( x ⋅ y ) = d d x ( x ) ⋅ y + x ⋅ d y d x The following derivative formulas are used: d d x ( cos x ) = − sin x d d x ( e x ) = e x Calculation: Consider the function y ( x ) = cos ( e x ) + e x cos x . Represent the function in the form of d y d x . d d x [ cos ( e x ) + e x cos x ] Separate the terms of the derivative of function. d d x [ cos ( e x ) ] + d d x [ e x cos x ] Then consider the first expression d d x [ cos ( e x ) ]

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ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 9.2, Problem 29E

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To calculate: The derivative of y(x)=cos(ex)+excosx.

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Chapter 9.2, Problem 28E

Chapter 9.2, Problem 30E

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Chapter 9 Solutions

Applied Calculus

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The derivative of y ( x ) = cos ( e x ) + e x cos x .

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Chapter 9 Solutions