If you use the $\log$ property for expressions of the form $\log \left(\frac{m}{n}\right)$ and then take the derivative of $f(x)=\ln \left(\frac{e^{x}-e^{3 x}}{e^{-2 x}+e^{-3 x}}\right)$, you obtain... A. $\frac{-2}{e^{x}-e^{3 x}}-\frac{5}{e^{-2 x}+e^{-3 x}}$ B. $\frac{-5 e^{x}+4}{e^{x}-1}$ C. $\frac{-5 e^{x}+4}{-e^{x}-1}$ D. $\frac{e^{x}-e^{3 x}(3)}{e^{x}-e^{3 x}}-\frac{e^{-2 x}(-2)+e^{-3 x}(-3)}{e^{-2 x}+e^{-3 x}}$ E. $-\frac{-5 e^{x}+4}{e^{x-1}}$ F. $\frac{e^{x}-e^{3 x}(3)}{e^{x}-e^{3 x}}+\frac{e^{-2 x}(-2)+e^{-3 x}(-3)}{e^{-2 x}+e^{-3 x}}$

Step 1 ：First, we simplify the function using the property of logarithms that \(\log \left(\frac{m}{n}\right) = \log(m) - \log(n)\). This will simplify the derivative calculation.

Step 2 ：After simplifying, we get \(f(x) = \log((1 - e^{x})e^{4x})\).

Step 3 ：Next, we take the derivative of the function using the chain rule and the derivative of the natural logarithm function, which is \(\frac{1}{x}\).

Step 4 ：The derivative of the function is \((4(1 - e^{x})e^{4x} - e^{5x})e^{-4x}/(1 - e^{x})\).

Step 5 ：Finally, we simplify this expression to match one of the given options. The simplified derivative of the function is \(\frac{5e^{x} - 4}{e^{x} - 1}\).

Step 6 ：\(\boxed{\text{Final Answer: The derivative of the function } f(x)=\ln \left(\frac{e^{x}-e^{3 x}}{e^{-2 x}+e^{-3 x}}\right) \text{ is } \frac{5e^{x} - 4}{e^{x} - 1}}\)