1. Second partials

Find second partials ( $f_{vv}$ and $f_{uv}$):

$f(u, v) = 5ln(u^2 + v^2)$

$f_{v} = \frac{10v}{u^2 + v^2}$

$f_{vu} = -1(u^2 + v^2)^{-2}(2u)10v$

$f_{vu} = - \frac{20uv}{(u^2 + v^2)^2}$

the correct answer is $f_{uv} = - \frac {40uv}{(u^2 + v^2)^2}$

Where did I go wrong finding $f_{uv}$?

2. Originally Posted by Macleef
Find second partials ( $f_{vv}$ and $f_{uv}$):

$f(u, v) = 5ln(u^2 + v^2)$

$f_{v} = \frac{10v}{u^2 + v^2}$

$f_{vu} = -1(u^2 + v^2)^{-2}(2u)10v$

$f_{vu} = - \frac{20uv}{(u^2 + v^2)^2}$

the correct answer is $f_{uv} = - \frac {40uv}{(u^2 + v^2)^2}$

Where did I go wrong finding $f_{uv}$?
Hi

$f_{v} = \frac{10v}{u^2 + v^2}$

$f_{vu} = \frac{\partial}{\partial u} \left(\frac{10v}{u^2 + v^2}\right) = -\frac{20uv}{(u^2 + v^2)^2}$