Explanation Given infromation: The given function is f ( t ) = ( 2 t + 1 ) ( t + 1 ) 3 . 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 ) The formula to calculate the differential of a function h ( x ) = [ g ( x ) f ( x ) ] by Quotient Rule is, h ′ ( x ) = f ( x ) g ′ ( x ) − f ′ ( x ) g ( x ) f 2 ( x ) Calculation: The given function is, f ( t ) = ( 2 t + 1 ) ( t + 1 ) 3 (1) Differentiate equation (1) with respect to t on both sides to evaluate f ′ ( t ) . f ′ ( t ) = ( 2 t + 1 ) ′ ( t + 1 ) 3 − ( 2 t + 1 ) [ ( t + 1 ) 3 ] ′ ( t + 1 ) 6 x

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 30RE

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To find: The derivative of the given function.

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Chapter 3, Problem 29RE

Chapter 3, Problem 31RE

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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The derivative of the given function.

Solution Summary: The author explains the formula to calculate the differential of a function by General Power Rule.

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To find: The derivative of the given function.

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Chapter 3 Solutions