Explanation Given information: The given function is f ( x ) = ( x 3 + x + 1 ) 2 . Formula used: The formula to calculate the differential of a function h ( x ) = [ g ( x ) ] n by General Power Rule is, h ′ ( x ) = n [ g ( x ) ] n − 1 ⋅ g ′ ( x ) The formula to calculate the differential of a function h ( x ) = [ g ( x ) f ( x ) ] by Product Rule is, h ′ ( x ) = f ( x ) g ′ ( x ) + f ′ ( x ) g ( x ) Calculation: The given function is, f ( x ) = ( x 3 + x + 1 ) 2 (1) Differentiate equation (1) with respect to x on both sides to evaluate f ′ ( x ) . f ′ ( x ) = d d x ( x 3 + x + 1 ) 2 = 2 ( x 3 + x + 1 ) 2 − 1 d d x ( x 3 + x + 1 ) [ Use General Power Rule d d x ( x n ) = n x n − 1 , n > 0 ] = 2 ( x 3 + x + 1 ) ( 3 x 3 − 1 + 1 ) [ Use General Power Rule d d x ( x n ) = n x</

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

10th Edition

ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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Chapter 3, Problem 34RE

To determine

The second derivative of given function.

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Chapter 3, Problem 33RE

Chapter 3, Problem 35RE

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Chapter 3 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

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The second derivative of given function.

Solution Summary: The author explains the second derivative of given function. The formula to calculate the differential of a function is, h(x)=n left.

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