Find y' y = 3x-2 2x+3

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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Question
Find y'
y =
y":
"=
3x-2
2x+3
Transcribed Image Text:Find y' y = y": "= 3x-2 2x+3
Expert Solution
Step 1: Rules of derivatives

Given Function

y=fraction numerator 3 x minus 2 over denominator 2 x plus 3 end fraction

(i) fraction numerator d space over denominator d x end fraction left parenthesis x to the power of n space end exponent right parenthesis equals n x to the power of n minus 1 end exponent

(ii) fraction numerator d space over denominator d x end fraction left parenthesis c o n s tan t right parenthesis equals 0

(iii) fraction numerator d space over denominator d x end fraction left parenthesis a over b right parenthesis equals fraction numerator b cross times fraction numerator d space over denominator d x end fraction left parenthesis a right parenthesis minus a cross times fraction numerator d space over denominator d x end fraction left parenthesis b right parenthesis over denominator b squared end fraction

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