Explanation Given: The function, f ( x ) = 3 + x 2 x . 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 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 Derivative of any constant C is zero, that is, d d x ( C ) = 0 Calculation: In order to find the derivatives of the given function f ( x ) = 3 + x 2 x , use the quotient rule and chain rule of derivatives and simplify further as shown below: f ' ( x ) = d d x ( 3 + x 2 x ) = ( 2 x ) ⋅ d d x ( 3 + x ) − ( 3 + x ) ⋅ d d x ( 2 x ) ( 2 x ) 2 = ( 2 x ) ⋅ [ d d x ( 3 ) + d d x ( x ) ] − ( 3 + x ) ⋅ 2 d d x ( x ) 4 x 2 = ( 2 x ) ⋅ [ ( 0 ) + (</

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

3rd Edition

ISBN: 9780840064189

Author: Frederick R. Adler

Publisher: Cengage Learning

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Chapter 2.7, Problem 17E

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The firstand second derivativesof the function, f(x)=3+x2x .

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Chapter 2.7, Problem 16E

Chapter 2.7, Problem 18E

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Chapter 2 Solutions

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

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The firstand second derivativesof the function, f ( x ) = 3 + x 2 x .

Solution Summary: The author explains the quotient rule and chain rule of derivatives.

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The firstand second derivativesof the function, f(x)=3+x2x .

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Chapter 2 Solutions