# Calculate Derivative? Square root?

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• Jul 20th 2009, 07:30 PM
Brazuca
Calculate Derivative? Square root?
http://img43.imageshack.us/img43/6099/squarej.jpg
I circled the part I didn't understand when solving this equation.

When I did it I turned U into 6^(1/2) and DU into 3X^(-1/2)
So I understand where the (1/1+6x), but I don't understand the rest.
• Jul 20th 2009, 07:45 PM
Random Variable
use the first fundamental theorem of calculus and the chain rule

$\frac {d}{dx} \int_{0}^{\sqrt{6x}} \frac {dt}{1+t^{2}} = \frac {1}{1+(\sqrt{6x})^2} \frac {d}{dx} \sqrt{6x}$
• Jul 20th 2009, 08:00 PM
Brazuca
I still don't understand where the [(Squareroot of 6) / 2 (Square root of X)] comes from.
• Jul 20th 2009, 08:12 PM
Random Variable
Quote:

Originally Posted by Brazuca
I still don't understand where the [(Squareroot of 6) / 2 (Square root of X)] comes from.

$\sqrt{6x}= \sqrt{6} \sqrt{x}$

so $\frac {d}{dx} \sqrt{6} \sqrt{x} = \sqrt{6} \ \frac {d}{dx} \sqrt{x} = \sqrt{6} \ \frac {1}{2} \frac {1}{\sqrt{x}}$