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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: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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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