Explanation Given: The function, f ( x ) = 1 + 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 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 given polynomial function f ( x ) = 1 + x 2 + x , use the quotient rule of derivatives and simplify further using the power rule of derivatives as shown below, f ' ( x ) = d d x ( 1 + x 2 + x ) = ( 2 + x ) ⋅ d d x ( 1 + x ) − ( 1 + x ) ⋅ d d x ( 2 + x ) ( 2 + x ) 2

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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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 2.6, Problem 7E

To determine

The derivative of the function, f(x)=1+x2+x using the quotient rule.

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Chapter 2.6, Problem 6E

Chapter 2.6, Problem 8E

Chapter 2 Solutions

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

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The derivative of the function, f ( x ) = 1 + x 2 + x using the quotient rule .

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

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The derivative of the function, f(x)=1+x2+x using the quotient rule.

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Chapter 2 Solutions