Find the derivative of the function.
\[
\begin{array}{c}
g(x)=2(4-7 x)^{4^{*}} \\
g^{\prime}(x)=\square
\end{array}
\]

Step 1 ：Identify the outer and inner functions. Here, the outer function is \(f(u)=2u^4\) and the inner function is \(u=4-7x\).

Step 2 ：Find the derivative of the outer function. The derivative of \(f(u)=2u^4\) with respect to \(u\) is \(f'(u)=8u^3\).

Step 3 ：Find the derivative of the inner function. The derivative of \(u=4-7x\) with respect to \(x\) is \(u'=-7\).

Step 4 ：Apply the chain rule. The chain rule states that \(g'(x)=f'(u) \cdot u'\). Substituting the derivatives we found in steps 2 and 3, we get \(g'(x)=8u^3 \cdot -7\).

Step 5 ：Substitute \(u=4-7x\) back into the derivative to get the derivative in terms of \(x\). So, \(g'(x)=8(4-7x)^3 \cdot -7\).

Step 6 ：Simplify the derivative. So, \(g'(x)=-56(4-7x)^3\).

Step 7 ：\(\boxed{g'(x)=-56(4-7x)^3}\) is the derivative of the function \(g(x)=2(4-7x)^4\).