# Second Partial Derivative/Examples

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## Examples of Second Partial Derivatives

### Example: $u + \ln u = x y$

Let $u + \ln u = x y$ be an implicit function.

Then:

$\dfrac {\partial^2 u} {\partial y \partial x} = \dfrac {\partial^2 u} {\partial x \partial y} = \dfrac u {u + 1} + \dfrac {x y u} {\paren {u + 1}^2}$