Explanation Given information: The function is f ( x ) = ( x + 1 x − 1 ) 5 Formula used: (1) For the derivative of division of two functions, the quotient rule is, h ( x ) = [ f ( x ) g ( x ) ] h ′ ( x ) = g ( x ) f ′ ( x ) − f ( x ) g ′ ( x ) [ g ( x ) ] 2 (2) If the function f is differentiable and h ( x ) = [ f ( x ) ] n ( n , a real number ) , then chain rule for power function is, h ′ ( x ) = d d x [ f ( x ) ] n = n [ f ( x ) ] n − 1 f ′ ( x ) Calculation: Use chain rule of differentiation for power function to evaluate the derivative of f ( x ) . f ′ ( x ) = d d x [ ( x + 1 x − 1 ) 5 ] = 5 ( x + 1 x − 1 ) 5 − 1 d d x ( x + 1 x − 1 ) = 5 ( x + 1 x − 1 ) 4 d d x ( x + 1 x − 1 ) Use quotient rule for above derivative function

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 3.3, Problem 34E

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The derivative of the given function.

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Chapter 3.3, Problem 33E

Chapter 3.3, Problem 35E

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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

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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Volume of a Cylinder The volume of a...Ch. 3.6 - Prob. 40E Ch. 3.6 - Prob. 41E Ch. 3.6 - Prob. 42E Ch. 3.6 - Prob. 43E Ch. 3.6 - Prob. 44E Ch. 3.6 - Prob. 45E Ch. 3.6 - Prob. 46E Ch. 3.6 - Prob. 47E Ch. 3.6 - PRODUCTION FUNCTION FOR A FURNITURE COMPANY The...Ch. 3.6 - Prob. 49E Ch. 3.6 - Prob. 50E Ch. 3.6 - Prob. 51E Ch. 3.6 - Prob. 52E Ch. 3.6 - Prob. 53E Ch. 3.6 - Prob. 54E Ch. 3.6 - Prob. 55E Ch. 3.6 - Prob. 56E Ch. 3.6 - Prob. 57E Ch. 3.6 - Prob. 58E Ch. 3.6 - Prob. 59E Ch. 3.6 - Prob. 60E Ch. 3.6 - Prob. 61E Ch. 3.6 - Prob. 62E Ch. 3.6 - Prob. 63E Ch. 3.6 - Prob. 64E Ch. 3.6 - Prob. 65E Ch. 3.6 - 66. 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The derivative of the given function.

Solution Summary: The author calculates the derivative of the function f(x)= (x+1 x-1 )5.

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Chapter 3 Solutions