1. Determine the derivatives of the following functionsIllustrative Example: Determine the derivative of y = x² + 2x + 1Solution:y+Ay = (x + Ax)² + 2(x + Ax) + 1Ay = (x + Ax)² + 2(x + Ax) + 1-y DUT y = x + 2x + 1Ay = (x + Ax)² + 2(x + Ax) +1 − (x² + 2x + 1)Ay = x² + 2xAx + Ax² + 2x + 2Ax+1-x² - 2x - 1Ay = 2xAx + Ax² + 2AxAyAxAy= 2x + Δx + 2lim =Ax-0 Axy' =dydxAPIElim 2x + Ax + 2 = 2x +0+2Ax-0= 2x + 2(b) y = √2-3xVERSITERSITEDNICAT

Answered: (b) y = √2-3x

Math

Calculus

(b) y = √2-3x

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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Question

1. Determine the derivatives of the following functions
Illustrative Example: Determine the derivative of y = x² + 2x + 1
Solution:
y+Ay = (x + Ax)² + 2(x + Ax) + 1
Ay = (x + Ax)² + 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 + 2Ax
Ay
Ax
Ay
= 2x + Δx + 2
lim =
Ax-0 Ax
y' =
dy
dx
APIE
lim 2x + Ax + 2 = 2x +0+2
Ax-0
= 2x + 2
(b) y = √2-3x
VERSIT
ERSIT
EDNICAT

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