Find the derivative of the function.
\[
s=t^{12} \ln |t|
\]

Step 1 ：Understand the problem: We are asked to find the derivative of the function \(s = t^{12} \ln|t|\). This is a product of two functions, \(t^{12}\) and \(\ln|t|\), so we will need to use the product rule for differentiation.

Step 2 ：Apply the product rule: The product rule states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.

Step 3 ：Differentiate \(t^{12}\): The derivative of \(t^{12}\) with respect to \(t\) is \(12t^{11}\).

Step 4 ：Differentiate \(\ln|t|\): The derivative of \(\ln|t|\) with respect to \(t\) is \(1/t\).

Step 5 ：Apply the product rule: So, the derivative of \(s = t^{12} \ln|t|\) is \((12t^{11} \ln|t|) + (t^{12} \cdot 1/t)\).

Step 6 ：Simplify the result: This simplifies to \(12t^{11} \ln|t| + t^{11}\).

Step 7 ：Check the result: The derivative of \(s = t^{12} \ln|t|\) is \(12t^{11} \ln|t| + t^{11}\). This is the simplest form of the derivative and it meets the requirements of the problem.

Step 8 ：\(\boxed{12t^{11} \ln|t| + t^{11}}\) is the final answer.