Differentiate from first principles

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Homework Help Overview

The problem involves differentiating the function (x+1)^(1/2) from first principles with respect to x. The original poster presents the limit definition of the derivative and their initial attempt at simplification.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss methods for simplifying the limit expression, with one suggesting the use of a specific algebraic identity to aid in the simplification process. Others provide general guidance on simplifying the fraction and approaching the limit.

Discussion Status

The discussion has seen participants offering suggestions for simplification techniques. The original poster indicates they have successfully completed the task, suggesting a productive exchange of ideas, though no detailed consensus on methods has been reached.

Contextual Notes

No specific constraints or missing information have been noted in the discussion.

auru
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Homework Statement



Differentiate (x+1)^1/2 from first principles with respect to x.

Homework Equations



f'(x) = Lim h→0 [f(x+h) - f(x)]/h

The Attempt at a Solution



f'(x) = Lim h→0 [f(x+h) - f(x)]/h
f'(x) = Lim h→0 [(x+h+1)^1/2 - (x+1)^1/2]/h

I'm unsure how to simplify from there.
 
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Use the equality

[tex](x-a)(x+a)=x^2 - a^2[/tex]

to simplify the limit.
 
Simplify the fraction, let h go to zero and you're done.
 
I've done it now, thanks!
 

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