$\displaystyle \frac{d}{dx} \frac{1}{\sqrt{x}}$

I feel retarded. I know how to find derivatives using the power rule and such but I'm having the hardest time doing this one :(

Please help.

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- Sep 19th 2010, 12:31 PMchickeneaterguyDefinition of a derivative to find....
$\displaystyle \frac{d}{dx} \frac{1}{\sqrt{x}}$

I feel retarded. I know how to find derivatives using the power rule and such but I'm having the hardest time doing this one :(

Please help. - Sep 19th 2010, 12:42 PMPlato
It is just algebra.

$\displaystyle \displaystyle

\frac{1}

{{\sqrt {x + h} }} - \frac{1}

{{\sqrt x }} = \frac{{\sqrt x - \sqrt {x + h} }}

{{\sqrt x \sqrt {x + h} }} = \frac{{ - h}}

{{\sqrt x \sqrt {x + h} \left( {\sqrt x + \sqrt {x + h} } \right)}}

$