Explanation Given information: The function is f ( x ) = x x 2 − 4 − x − 1 x 2 + 4 . Formula used : The quotient rule of differentiation is, f ′ ( x ) = d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) [ g ( x ) ] 2 The above formula is defined when the denominator g ( x ) ≠ 0 . Calculation: The derivative of given function is, f ′ ( x ) = d d x ( x x 2 − 4 − x − 1 x 2 + 4 ) = d d x ( x x 2 − 4 ) − d d x ( x − 1 x 2 + 4 ) ( Apply distributive property ) Use the quotient formula of differentiation in the above derivative function. f ′ ( x ) = d d x ( x x 2 − 4 ) − d d x ( x − 1 x 2 + 4 ) = [ ( x 2 − 4 ) ⋅ d d x ( x ) − x ⋅ d d x ( x 2 − 4 ) ( x 2 − 4 ) 2 ] − [ ( x 2 + 4 ) ⋅ d d x ( x − 1 ) − ( x − 1 ) ⋅ d d x ( x 2 + 4 ) ( x 2 + 4 ) 2 ] = [ ( x 2 − 4 ) ( 1 ) − x ( 2 x ) ( x 2 − 4 ) 2 ] − [ ( x 2 + 4 ) ( 1 − 0 ) − ( x − 1 ) ( 2 x ) ( x 2 + 4 ) 2 ] = − ( x 2 + 4 ) ( x 2 − 4 ) 2 − ( − x 2 + 2 x + 4 ) ( x 2 + 4 ) 2 Further solve the above expression to get the value of f ′ ( x )

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 3.2, Problem 29E

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To find: The derivative of given function.

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Chapter 3.2, Problem 28E

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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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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 given function.

Solution Summary: The author explains the derivative of function f(x) and the quotient rule of differentiation.

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Chapter 3 Solutions