Explanation Given: The function is f ( x ) = 2 x − 1 . Definition used: The first derivative of the function is the differentiation of the function, f ′ ( x ) = d d x f ( x ) (1) The second derivative of the function is the differentiation of the first derivative of the function, f ″ ( x ) = d d x f ′ ( x ) (2) The chain rule stated that the derivation of the function, f ( g ( x ) ) is f ′ ( g ( x ) ) ⋅ g ′ ( x ) . Formula used: The power rule of the derivatives is, d d x a x n = a ⋅ n ⋅ x n − 1 Calculation: Substitute 2 x − 1 for f ( x ) in equation (1) to find the first derivative of the function, f ′ ( x ) = d d x [ 2 x − 1 ] = 1 2 2 x − 1 ⋅ d d x ( 2 x − 1 ) ( Use chain rule ) = 2 2 2 x − 1

Applied Calculus for the Managerial, Life, and Social Sciences

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ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 3.5, Problem 20E

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The first and the second derivative of the function.

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Chapter 3.5, Problem 19E

Chapter 3.5, Problem 21E

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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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The first and the second derivative of the function.

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