\[ f(x)=\ln \left(e^{x}-5 x\right) \] (a) Find $f^{\prime}(x)$. \[ f^{\prime}(x)= \] (b) Find $f^{\prime}(0)$. \[ f^{\prime}(0)= \]

Step 1 ：Given the function \(f(x)=\ln \left(e^{x}-5 x\right)\)

Step 2 ：We need to find the derivative of the function, \(f^{\prime}(x)\), and the value of the derivative at \(x=0\), \(f^{\prime}(0)\)

Step 3 ：The derivative of the function is found using the chain rule of differentiation, which gives \(f^{\prime}(x)=\frac{e^{x}-5}{e^{x}-5x}\)

Step 4 ：Substituting \(x=0\) into the derivative function gives \(f^{\prime}(0)=-4\)

Step 5 ：Final Answer: The derivative of the function \(f(x)\) is \(\boxed{f^{\prime}(x)=\frac{e^{x}-5}{e^{x}-5x}}\) and the value of the derivative at \(x=0\) is \(\boxed{f^{\prime}(0)=-4}\)