# Second Partial Derivative/Examples

### Example: $u + \ln u = x y$
Let $u + \ln u = x y$ be an implicit function.
$\dfrac {\partial^2 u} {\partial y \partial x} = \dfrac {\partial^2 u} {\partial x \partial y} = \dfrac u {u + 1} + \dfrac {x y u} {\paren {u + 1}^2}$