Step-by-step Solution:

\(f(x)=x^{x}\) \[\] \(f^{\prime}(x)=x^{x}(1+\log x)\) \[\] for decreasing function \[\] \(f^{\prime}(x) < 0 \Rightarrow x^{x}(1+\log x) < 0\) \[\] \(\Rightarrow 1+\log x < 0 \Rightarrow \log x < -1\) \[\] \(\Rightarrow x < e^{-1}\) and \(\mathrm{x}>0\) interval is \(\left(0 \frac{1}{e}\right)\) \[\] Choice (C)\[\]