Explanation Given information: The given function is, f ( x ) = 1 x + 1 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 ) Calculation: The given function is, f ( x ) = 1 x + 1 = ( x + 1 ) − − 1 2 (1) Differentiate equation (1) with respect to x on both sides to evaluate f ′ ( x ) . f ′ ( x ) = d d x ( x + 1 ) − − 1 2 = − 1 2 ( x + 1 ) − 1 2 − 1 ( x + 1 ) ′ [ Use General Power Rule d d x ( x n ) = n x n − 1 , n > 0 ] = − 1 2 ( x + 1 ) − 3 2 Again differentiate above equation with respect to x on the both sides, to evaluate f ″ ( x ) f ″ ( x ) = d d x [ − 1 2 ( x + 1 ) − 3 2 ] = − 1 2 ( − 3 2 ) ( x + 1 ) −

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 4BM

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To find: The first three derivatives of given function.

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Chapter 3, Problem 3BM

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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 first three derivatives of given function.

Solution Summary: The author explains the formula to calculate the differential of a function: f(x)=1sqrtx+1.

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To find: The first three derivatives of given function.

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Chapter 3 Solutions