1. Second partials

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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