Dirty Maxima

Calculus Level 5

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

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