Quick question

**Undefdisfigure** · October 19th 2007, 02:00 PM

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.

**Plato** · October 19th 2007, 02:36 PM

$u = \ln \left( {\sqrt {x^2 + y^2 } } \right) = \frac{{\ln \left( {x^2 + y^2 } \right)}}{2}$

$u_x = \frac{x}{{x^2 + y^2 }}\quad \quad u_{xx} = \frac{{y^2 - x^2 }}{{\left( {x^2 + y^2 } \right)^2 }}<br />$

**Undefdisfigure** · October 19th 2007, 03:14 PM

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...

**Plato** · October 19th 2007, 03:38 PM

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

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