Explanation Given: The function, y = e − 2 t cos ( 4 t ) . Concept Used: The product rule of derivatives: d d x [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) Chain rule, d d x ( f ( g ( x ) ) ) = f ' ( g ( x ) ) ⋅ g ' ( x ) Power rule of derivatives, d d x ( x n ) = n x n − 1 d d x ( e x ) = e x Derivative of any constant C is zero, that is, d d x ( C ) = 0 Calculation: In order to find the derivative of the function,useproduct rule and chain rule of derivatives and simplify further to get, y ' = d d t ( e − 2 t cos ( 4 t ) ) = e − 2 t ⋅ d d t ( cos ( 4 t ) ) + cos ( 4 t ) ⋅ d d t ( e − 2 t )

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Chapter 3.5, Problem 18E

To determine

The derivative of the function, y=e−2tcos(4t) .

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Chapter 3.5, Problem 17E

Chapter 3.5, Problem 19E

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The derivative of the function, y = e − 2 t cos ( 4 t ) .

Solution Summary: The author explains the product rule and chain rule of derivatives and simplify further to get the derivative of the function.

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The derivative of the function, y=e−2tcos(4t) .

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