What is the Derivative of y = √x at x = 1?

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To find the derivative of y = √x at x = 1, the limit formula lim x -> a = (f(x) - f(a)) / (x - a) is applied. The expression starts as (√x - 1) / (x - 1), but simplification is needed. A user suggests multiplying by the conjugate (√x + 1) to facilitate simplification. This approach leads to a clearer path for calculating the derivative. The discussion emphasizes the importance of algebraic manipulation in derivative calculations.
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I was asked to find the derivative of y=sqrtx at x=1

I need to use the formula

lim x -> a = f(x) - f(a) / (x-a) to find the derivative at x=1

I have..

sqrtx - 1 / (x - 1) BUT i can't simply it from there. Help!

THANKSZ.
 
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Okay:
\frac{\sqrt{x}-1}{x-1}=\frac{\sqrt{x}+1}{\sqrt{x}+1}\frac{\sqrt{x}-1}{x-1}=\frac{(\sqrt{x}+1)(\sqrt{x}-1)}{x-1}\frac{1}{\sqrt{x}+1}
Does that help you a bit?
 

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