Differentiate and simplify: $f(x)=\frac{\ln e^{x}}{e^{x}}$

Step 1 ：Given the function \(f(x)=\frac{\ln e^{x}}{e^{x}}\)

Step 2 ：We can simplify the function before differentiating. The natural logarithm of \(e^{x}\) is \(x\), so the function simplifies to \(f(x)=\frac{x}{e^{x}}\)

Step 3 ：This is a quotient of two functions, so we can use the quotient rule to differentiate it. The quotient rule is \(\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{vu'-uv'}{v^2}\), where \(u\) is the numerator function, \(v\) is the denominator function, \(u'\) is the derivative of \(u\), and \(v'\) is the derivative of \(v\)

Step 4 ：In this case, \(u=x\), \(v=e^{x}\), \(u'=1\), and \(v'=e^{x}\)

Step 5 ：Applying the quotient rule, we get \(f'(x)=\frac{e^{x}*1 - x*e^{x}}{(e^{x})^2}\)

Step 6 ：Simplifying the derivative, we get \(f'(x)=(1 - x)e^{-x}\)

Step 7 ：Final Answer: \(f'(x)=\boxed{(1 - x)e^{-x}}\)