Differentiate.
\[
y=\frac{\ln x}{x^{13}}
\]
\[
\frac{d y}{d x}=
\]

Step 1 ：Given the function \(y = \frac{\ln x}{x^{13}}\).

Step 2 ：We need to find the derivative of this function.

Step 3 ：We use the quotient rule for differentiation, which states that the derivative of a quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the square of the denominator.

Step 4 ：In this case, our numerator is \(\ln(x)\) and our denominator is \(x^{13}\).

Step 5 ：Applying the quotient rule, we get \(\frac{d y}{d x} = -\frac{13 \ln x}{x^{14}} + \frac{1}{x^{14}}\).

Step 6 ：\(\boxed{\frac{d y}{d x} = -\frac{13 \ln x}{x^{14}} + \frac{1}{x^{14}}}\) is the final answer.