Explanation Given: The function is g ( s ) = 3 s − 2 . Definition used: The first derivative of the function is the differentiation of the function, g ′ ( s ) = d d s g ( s ) (1) The second derivative of the function is the differentiation of the first derivative of the function, g ″ ( s ) = d d s g ′ ( s ) (2) The third derivative of the function is the differentiation of the second derivative of the function, g ‴ ( s ) = d d s g ″ ( s ) (3) Formula used: The power rule of the derivatives is, d d x a x n = a ⋅ n ⋅ x n − 1 Calculation: Rewrite the given function as, g ( s ) = 3 s − 2 = ( 3 s − 2 ) 1 / 2 Substitute ( 3 s − 2 ) 1 / 2 for g ( s ) in equation (1) to find the first derivative of the function, g ′ ( s ) = d d s ( 3 s − 2 ) 1 / 2 = 1 2 ( 3 s − 2 ) − 1 / 2 d d s ( 3 s − 2 ) ( Use chain rule ) = 1 2 ( 3 s − 2 ) − 1 / 2 ( 3 ) ( Use power rule ) = 3 2 ( 3 s − 2 ) − 1 / 2 Substitute 3 2 ( 3 s − 2 ) − 1 / 2 for g ′ ( s ) in equation (2) to find the second derivative of the function, g ″ ( s ) = d d s [ 3 2 ( 3 s − 2 ) − 1<

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 3.5, Problem 25E

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The third derivative of the function.

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Chapter 3.5, Problem 24E

Chapter 3.5, Problem 26E

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In Exercises 43 and 44, find all derivatives of the function. 3 44. y = 120 43. y = 2

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The third derivative of the function.

Solution Summary: The author explains that the third derivative of the function is 818(3s-2)-5/2.

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Chapter 3 Solutions