Answer
\begin{array}{|c|c|c|c|c|c|} \hline x & {-4} & {-2} & {0} & {2} & {4} & {8} \\ \hline y & {2} & {0} & {4} & {4} & {6} & {8} \\ \hline
\hline \frac{d y }{ d x} & {-2\sqrt 2} & {-2} & {0} & {0} & {-2 \sqrt{2}} & {-8} \\ \\ \hline
\end{array}
Work Step by Step
Given$$\dfrac{dy}{dx}=x \cos \frac{\pi y}{8 }$$ and
\begin{array}{|c|c|c|c|c|c|}\hline x & {-4} & {-2} & {0} & {2} & {4} & {8} \\ \hline y & {2} & {0} & {4} & {4} & {6} & {8} \\ \hline \dfrac{d y }{d x } & { } & { } & { } & { } & { } & { } \\ \hline\end{array}
$$$$
Since the $1^{st}$ derivative $(\dfrac{dy}{dx}) $ mean the slope, so by substituting by the values of points $(x,y)$, we get
\begin{array}{|c|c|c|c|c|c|} \hline x & {-4} & {-2} & {0} & {2} & {4} & {8} \\ \hline y & {2} & {0} & {4} & {4} & {6} & {8} \\ \hline \frac{d y }{ d x} & {-4 \cos \frac{\pi }{4 }} & {-2 \cos 0} & {0} & {2 \cos \frac{\pi }{2 }} & {4 \cos \frac{3 \pi }{4 }} & {8 \cos \pi } \\ \\ \hline
\hline \frac{d y }{ d x} & {-2\sqrt 2} & {-2} & {0} & {0} & {-2 \sqrt{2}} & {-8} \\ \\ \hline
\end{array}