Explanation Given: The given equation is y = 20 t 4 / 5 − 6 t 2 / 3 Formula used: Power Rule: ( x n ) ' = n x n − 1 Calculation: Here, let us first find the first derivative of the given equation. The first derivative if y ' = ( 20 t 4 / 5 − 6 t 2 / 3 ) ' = 4 5 × 20 t 4 5 − 1 − 2 3 × 6 t 2 3 − 1 = 16 t − 1 5 − 4 t − 1 3 . Now, we know that the second derivative is the derivative of the first derivative. Therefore, we get the second derivative as y ' ' = ( y ' ) ' = ( 16 t − 1 5 − 4 t − 1 3 ) ' = − 1 5 × 16 t − 1 5 − 1 − − 1 3 × 4 t − 1 3 − 1 = − 16 5 t − 6 2 + 4 3 t − 4 3

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 3.5, Problem 7E

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The second and third derivatives of the given equation

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Ch. 3.1 - Prob. 1PQ Ch. 3.1 - Prob. 2PQ Ch. 3.1 - Prob. 3PQ Ch. 3.1 - Prob. 4PQ Ch. 3.1 - Prob. 5PQ 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

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The second and third derivatives of the given equation

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