Suppose that $\mathrm{x}$ and $\mathrm{y}$ are related by the equation \[ y=8+\log _{10}(5 / x) \] Compute $\frac{d y}{d x}$ and evaluate it at $\mathrm{x}=1.3$. Enter your answer as a decimal. Round to three decimal places (as needed).

Step 1 ：Suppose that \(x\) and \(y\) are related by the equation \(y=8+\log _{10}(5 / x)\).

Step 2 ：We are asked to compute \(\frac{d y}{d x}\) and evaluate it at \(x=1.3\).

Step 3 ：Using the properties of logarithms and the chain rule, we find that \(\frac{d y}{d x} = -\frac{5}{x^2 \ln(10)}\).

Step 4 ：Substituting \(x = 1.3\) into the derivative, we get \(\frac{d y}{d x} = -\frac{5}{(1.3)^2 \ln(10)}\).

Step 5 ：Calculating the above expression, we get \(\frac{d y}{d x} \approx -1.284894916873526\).

Step 6 ：Rounding to three decimal places, we get \(\frac{d y}{d x} \approx -1.285\).

Step 7 ：Final Answer: The derivative of the function \(y=8+\log _{10}(5 / x)\) evaluated at \(x=1.3\) is approximately \(\boxed{-1.285}\).