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.
$\displaystyle f(x)=\sqrt{x^2+n}$, 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?