Dirty Maxima

${ \left( \cos { x } \ln { \left( { x }^{ \frac { 1 }{ x } } \right) } -\frac { \cos { x } \log _{ 10 }{ x } }{ \ln { \left( \ln { x } \right) } } \right) }^{ \cos { x } }$ Find the maximum value of the expression above.