Explanation Given information: The given function is, f ( x ) = 1 2 x − 1 (1) Formula used: The formula to calculate the differential of a function h ( x ) = g [ f ( x ) ] by Chain Rule is, h ′ ( x ) = d d x g [ f ( x ) ] = g ′ [ f ( x ) ] f ′ ( x ) Calculation: Differentiate both sides of the equation (1) with respect to x by chain rule. f ′ ( x ) = d d x ( 1 2 x − 1 ) = d d x ( 2 x − 1 ) − 1 = − 1 ( 2 x − 1 ) − 1 − 1 d d x ( 2 x − 1 ) = − ( 2 x − 1 ) − 2 ( 2 ) Differentiate both sides of the above equation with respect to x by chain rule to find the second derivative. f ″ ( x ) = d d x ( − 2 ( 2 x − 1 ) − 2 ) = − 2 ( − 2 ( 2 x − 1 ) − 2 − 1 ) d d x ( 2 x − 1 ) = 4 ( 2 x − 1 ) − 3 ( 2 ) = 8 ( 2 x − 1 ) − 3 Differentiate both sides of the above equation with respect to x by chain rule to find the third derivative

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 3, Problem 51RE

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To find: The third derivative of the function and its domain.

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Chapter 3, Problem 50RE

Chapter 3, Problem 52RE

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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The third derivative of the function and its domain.

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Chapter 3 Solutions