Suppose $f(1)=2, f^{\prime}(1)=3, f(2)=1, f^{\prime}(2)=2$, and $g(1)=3, g^{\prime}(1)=5, g(2)=1, g^{\prime}(2)=4$. If $S(x)=f(x)+g(x)$, find the value of $S^{\prime}(1)$.

Step 1 ：Given that $f(1)=2, f^{\prime}(1)=3, f(2)=1, f^{\prime}(2)=2$, and $g(1)=3, g^{\prime}(1)=5, g(2)=1, g^{\prime}(2)=4$.

Step 2 ：Define $S(x)=f(x)+g(x)$.

Step 3 ：Then, the derivative of $S(x)$, denoted as $S^{\prime}(x)$, is equal to the sum of the derivatives of $f(x)$ and $g(x)$, i.e., $S^{\prime}(x)=f^{\prime}(x)+g^{\prime}(x)$.

Step 4 ：Substitute $x=1$ into the equation, we get $S^{\prime}(1)=f^{\prime}(1)+g^{\prime}(1)$.

Step 5 ：Substitute the given values $f^{\prime}(1)=3$ and $g^{\prime}(1)=5$ into the equation, we get $S^{\prime}(1)=3+5$.

Step 6 ：Simplify the right hand side of the equation, we get $S^{\prime}(1)=\boxed{8}$.