Explanation Given information: The function is f ( x ) = ( x 3 + 2 x + 1 ) ( 2 + 1 x 2 ) . Formula used : (1). The product rule of differentiation is, f ′ ( x ) = d d x [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) (2). The power rule of derivate is d d x ( x n ) = n x n − 1 . Calculation: Use product rule of differentiation to find the derivative of the function. f ′ ( x ) = d d x [ ( x 3 + 2 x + 1 ) ( 2 + 1 x 2 ) ] = ( x 3 + 2 x + 1 ) d d x ( 2 + 1 x 2 ) + ( 2 + 1 x 2 ) d d x ( x 3 + 2 x + 1 ) (1) Use the power rule to find the derivate of term ( 2 + 1 x 2 ) . d d x ( 2 + 1 x 2 ) = d d x ( 2 ) + d d x ( 1 x 2 ) = 0 + d d x ( x − 2 ) = − 2 x − 3 = − 2 x 3 Use the power rule to find the derivate of term ( x 3 + 2 x + 1 )

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 14E

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To find: The derivative of given function.

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Chapter 3.2, Problem 13E

Chapter 3.2, Problem 15E

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Find the derivative of the function. Ax) = 7x? (6 - 9x)* O (-14x)(6 - 9x) (7x-6) O (-42x)(6- 9x)(9x- 2) O 56x(6 - 9x) O (14x)(6- 9x) (7x - 6) (-21x²)(6 - 92)* (3x - 6)

Determine whether the function is not differentiable using differentiability and continuity, and show the complete solution, thank you so much

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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AUTO TRANSMISSIONS .AND FUEL ECONOMY In trying to...Ch. 3.5 - Prob. 32E Ch. 3.5 - Prob. 33E Ch. 3.5 - Prob. 34E Ch. 3.5 - Prob. 35E Ch. 3.5 - Prob. 36E Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - Prob. 40E Ch. 3.5 - Prob. 41E Ch. 3.5 - Prob. 42E Ch. 3.5 - Prob. 43E Ch. 3.5 - Prob. 44E Ch. 3.5 - Prob. 45E Ch. 3.5 - Prob. 46E Ch. 3.5 - Prob. 47E Ch. 3.5 - Prob. 48E Ch. 3.5 - Prob. 49E Ch. 3.5 - Prob. 50E Ch. 3.5 - Prob. 1TE Ch. 3.5 - Prob. 2TE Ch. 3.5 - Prob. 3TE Ch. 3.5 - Prob. 4TE Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - Prob. 6TE Ch. 3.5 - Prob. 7TE Ch. 3.5 - Prob. 8TE Ch. 3.6 - Prob. 1CQ Ch. 3.6 - Prob. 2CQ Ch. 3.6 - Prob. 3CQ Ch. 3.6 - Prob. 4CQ Ch. 3.6 - Prob. 1E Ch. 3.6 - Prob. 2E Ch. 3.6 - Prob. 3E Ch. 3.6 - Prob. 4E Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - Prob. 8E Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Prob. 11E Ch. 3.6 - Prob. 12E Ch. 3.6 - Prob. 13E Ch. 3.6 - Prob. 14E Ch. 3.6 - Prob. 15E Ch. 3.6 - 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The derivative of given function.

Solution Summary: The author explains how to find the derivative of a given function by using the product rule of differentiation.

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To find: The derivative of given function.

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Chapter 3 Solutions