Differentiate the function.
\[
\begin{array}{r}
y=\sqrt{x}(x-8) \\
y^{\prime}=\square
\end{array}
\]

Step 1 ：Given the function \(y = \sqrt{x}(x - 8)\).

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

Step 3 ：We can use the product rule for differentiation, which states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function.

Step 4 ：In this case, the first function is \(\sqrt{x}\) and the second function is \((x - 8)\).

Step 5 ：Differentiating, we get \(y' = \sqrt{x} + \frac{x - 8}{2\sqrt{x}}\).

Step 6 ：So, the derivative of the function is \(\boxed{y' = \sqrt{x} + \frac{x - 8}{2\sqrt{x}}}\).