Question Suppose $h(x)=f(g(x))$. Given the table of values below, determine $h^{\prime}(-1)$. \begin{tabular}{|c|c|c|c|c|} \hline$x$ & $f(x)$ & $g(x)$ & $f^{\prime}(x)$ & $g^{\prime}(x)$ \\ \hline-1 & 3 & 2 & -7 & 10 \\ \hline 2 & 5 & 6 & 4 & 6 \\ \hline 4 & 7 & -3 & -5 & -5 \\ \hline \end{tabular} Do not include " $h^{\prime}(-1)=$ " in your answer. Provide your answer below:

Step 1 ：Given that \(h(x)=f(g(x))\), we can use the chain rule to find \(h^{\prime}(x)\). The chain rule states that \(h^{\prime}(x) = f^{\prime}(g(x)) \cdot g^{\prime}(x)\).

Step 2 ：Substitute \(x = -1\) into the equation, we get \(h^{\prime}(-1) = f^{\prime}(g(-1)) \cdot g^{\prime}(-1)\).

Step 3 ：From the table, we know that \(g(-1) = 2\) and \(g^{\prime}(-1) = 10\).

Step 4 ：Substitute these values into the equation, we get \(h^{\prime}(-1) = f^{\prime}(2) \cdot 10\).

Step 5 ：From the table, we know that \(f^{\prime}(2) = 4\).

Step 6 ：Substitute this value into the equation, we get \(h^{\prime}(-1) = 4 \cdot 10\).

Step 7 ：So, \(h^{\prime}(-1) = \boxed{40}\).