Can anyone help me out in finding the second and third derivitive of radicals like $\displaystyle \sqrt{x^2+3}$

Thanks, I can really use some help.

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- Sep 25th 2008, 02:58 PMskyslimitSecond/Third Derivitive
Can anyone help me out in finding the second and third derivitive of radicals like $\displaystyle \sqrt{x^2+3}$

Thanks, I can really use some help. - Sep 25th 2008, 03:05 PMJameson
$\displaystyle f(x)=\sqrt{x^2+n}$, where n is any constant.

Then using the power rule with the power being 1/2, $\displaystyle f'=\frac{1}{2}(x^2+n)^{-\frac{1}{2}} \times 2x=\frac{2x}{2\sqrt{x^2+n})}=\frac{x}{\sqrt{x^2+n} }$

Now for f'', use the quotient rule. Is this the point where you're having trouble or did this post clear something up? - Sep 25th 2008, 03:14 PMskyslimit
Im having more trouble finding a way to find the second derivative of that

- Sep 25th 2008, 06:07 PMJameson
Well the derivative of u/v is (vu'-vu')/v^2, so just follow the formula and you already know the derivative of v since v is f(x) :)

- Sep 25th 2008, 06:35 PMskyslimit
I broke the top and bottom of the first derivative into seaparate functions foruse in the product. But I end up with the same equation for the second derivitive as i got in the first. Is this correct?