Mysterious Function

Calculus Level 4

It is given that \(\sum _{ n=1 }^{ \infty }{ f^{ (n) }\left( x \right) = } f\left( x \right) \) for all values of \(x\), where \(f^{ (n) }\left( x \right)\) represents the \({ n }^{ th }\) derivative of \(f\left( x \right)\). If \(f(0)=1\), find the value of \(\ln { f\left( 2 \right) } \).

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