
Quick question
if I have u = ln(root(x^2 + y^2)) then in the first partial derivative d^2u/dx^2 (or Uxx in other words) should I get 2x/root(x^2 + y^2) or x/(x^2 + y^2)^3/2.
I need to remember what I have to do exactly and I won't ask too many questions like this as I would be spamming the boards.
Please reply soon, thanks.

$\displaystyle u = \ln \left( {\sqrt {x^2 + y^2 } } \right) = \frac{{\ln \left( {x^2 + y^2 } \right)}}{2}$
$\displaystyle u_x = \frac{x}{{x^2 + y^2 }}\quad \quad u_{xx} = \frac{{y^2  x^2 }}{{\left( {x^2 + y^2 } \right)^2 }}
$

Looks like I was wrong entirely. But how did you derive u= ln(root(x^2 + y^2)) = ln(x^2 + y^2)/2 Plato, or anybody else if they know...

$\displaystyle x > 0\quad \Rightarrow \quad \ln \left( {\sqrt x } \right) = \ln \left( {x^{\frac{1}{2}} } \right) = \left( {\frac{1}{2}} \right)\ln (x)
$