Explanation Given information: The function is f ( x ) = x + 3 x 3 x − 1 . 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: Use the quotient formula of differentiation and solve given function to get the value of its derivative. f ′ ( x ) = d d x ( x + 3 x 3 x − 1 ) = ( 3 x − 1 ) ⋅ d d x ( x + 3 x ) − ( x + 3 x ) ⋅ d d x ( 3 x − 1 ) ( 3 x − 1 ) 2 = ( 3 x − 1 ) ⋅ ( 1 + 3 ⋅ 1 2 ( x ) − 1 2 ) − ( x + 3 x ) ⋅ ( 3 − 0 ) ( 3 x − 1 ) 2 = ( 3 x − 1 ) ⋅ ( 1 + 3 2 x ) − ( x + 3 x ) ⋅ ( 3 − 0 ) ( 3 x − 1 ) 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 30E

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To find: The derivative of given function.

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Chapter 3.2, Problem 29E

Chapter 3.2, Problem 31E

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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 derivative of given function.

Solution Summary: The author explains how to find the derivative of a given function using the quotient formula of differentiation.

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To find: The derivative of given function.

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Chapter 3 Solutions