Find the derivative of the function.
\[
\begin{array}{r}
f(x)=(4-x)^{6} \\
f^{\prime}(x)=-6(4-x)^{5}
\end{array}
\]

Step 1 ：The problem is asking for the derivative of the function \(f(x)=(4-x)^{6}\). The derivative of a function measures how the function changes as its input changes. In this case, we want to know how the function \(f(x)\) changes as \(x\) changes.

Step 2 ：To find the derivative of the function, we can use the power rule for differentiation, which states that the derivative of \(x^n\) is \(nx^{n-1}\). However, since our function is in the form of \((4-x)^6\), we also need to use the chain rule for differentiation, which states that the derivative of a composition of functions is the derivative of the outer function times the derivative of the inner function.

Step 3 ：In this case, the outer function is \(u^6\) and the inner function is \(4-x\). The derivative of the outer function is \(6u^5\) and the derivative of the inner function is \(-1\).

Step 4 ：So, the derivative of the function \(f(x)\) is \(6u^5*(-1)\), where \(u=4-x\).

Step 5 ：The derivative of the function \(f(x)=(4-x)^{6}\) is \(\boxed{-6(4-x)^{5}}\).