The below data satisfies $Z=f(x,Y).$ Calculate the central derivative estimate for $f_y(1\mathrm{.}5,0).$

$x=\left[\begin{array}{ccccc}0& 0\mathrm{.}5& 1& 1\mathrm{.}5& 2\\ 0& 0\mathrm{.}5& 1& 1\mathrm{.}5& 2\\ 0& 0\mathrm{.}5& 1& 1\mathrm{.}5& 2\\ 0& 0\mathrm{.}5& 1& 1\mathrm{.}5& 2\\ 0& 0\mathrm{.}5& 1& 1\mathrm{.}5& 2\end{array}\right],Y=\left[\begin{array}{ccccc}-2& -2& -2& -2& -2\\ -1& -1& -1& -1& -1\\ 0& 0& 0& 0& 0\\ 1& 1& 1& 1& 1\\ 2& 2& 2& 2& 2\end{array}\right],Z=\left[\begin{array}{ccccc}0& 1& 2& -1& -2\\ 1& -2& 3& 4& 4\\ 0& 1& -3& -1& 3\\ 0& -2& 0& 1& 1\\ 0& 0& 1& 1& 0\end{array}\right]$

Answer: