Explanation Given: The function, f ( x ) = a x + b c x + d . Concept Used: The quotient rule of derivatives: d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) ( g ( x ) ) 2 Power rule of derivatives: d d x ( x n ) = n x n − 1 d d x ( e x ) = e x Calculation: In order to find the derivative of the given function, use the quotient rule of derivatives. Observe that the given function is a quotient of two functions ( a x + b ) and ( c x + d ) , where a , b , c , and d are constants. So, using the quotient rule and power rule of derivatives, it gives f ' ( x ) = d d x ( a x + b c x + d ) = ( c x + d ) ⋅

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.4, Problem 34E

To determine

The derivative of the function, f(x)=ax+bcx+d .

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Chapter 3.4, Problem 33E

Chapter 3.4, Problem 35E

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Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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The derivative of the function, f ( x ) = a x + b c x + d .

Solution Summary: The author explains how to find the derivative of the given function using the quotient rule of derivatives.

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The derivative of the function, f(x)=ax+bcx+d .

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