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1. Determine the derivatives of the following functions (a) y = (x² - 2)²

1. Determine the derivatives of the following functions (a) y = (x² - 2)²

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 3CR: Determine whether each of the following statements is true or false, and explain why. The derivative...
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1. Determine the derivatives of the following functions (a) y = (x² - 2)² SAPIE Illustrative Example: Determine the derivative of y = x² + 2x + 1 Solution: y + Ay = (x + Ax)² + 2(x + Ax) + 1 Ax Ay = (x + Ax)" + 2(x + Ax) + 1-y DUT y = x + 2x + 1 Ay = (x + Ax)² + 2(x + Ax) + 1 - (x² + 2x + 1) Ay = x² + 2xAx + Ax² + 2x + 2Ax+1-x² - 2x - 1 Ay = 2xAx + Ax² + 24x Ay Ay VOTINIVS = = 2x + 4x + 2 lim = lim 2x + Ax + 2 = 2x +0+2 Ax-0 Ax Ax-0 dy dx VERSITY: = 2x + 2 VERSIT NIGALA
Transcribed Image Text:1. Determine the derivatives of the following functions (a) y = (x² - 2)² SAPIE Illustrative Example: Determine the derivative of y = x² + 2x + 1 Solution: y + Ay = (x + Ax)² + 2(x + Ax) + 1 Ax Ay = (x + Ax)" + 2(x + Ax) + 1-y DUT y = x + 2x + 1 Ay = (x + Ax)² + 2(x + Ax) + 1 - (x² + 2x + 1) Ay = x² + 2xAx + Ax² + 2x + 2Ax+1-x² - 2x - 1 Ay = 2xAx + Ax² + 24x Ay Ay VOTINIVS = = 2x + 4x + 2 lim = lim 2x + Ax + 2 = 2x +0+2 Ax-0 Ax Ax-0 dy dx VERSITY: = 2x + 2 VERSIT NIGALA
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