Use first principles to differentiate the function f(x) = √√2x + 1

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. Use first principles to differentiate the function f(x) = √2x + 1
Transcribed Image Text:1. Use first principles to differentiate the function f(x) = √2x + 1
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Step 1: Given information

f left parenthesis x right parenthesis equals square root of 2 x plus 1 end root
f i r s t space p r i n c i p l e s space t o space d i f f e r e n t i a t e

f apostrophe left parenthesis x right parenthesis equals limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction

f left parenthesis x plus h right parenthesis equals square root of 2 left parenthesis x plus h right parenthesis plus 1 end root

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