I am trying to find the derivative $\frac{dy}{dx}$ from the following dataset,
x y
===============================
0 0.37646 + 0i
10 0.37074 + 0.065372i
20 0.35376 + 0.12876i
30 0.32603 + 0.18823i
40 0.28839 + 0.24198i
50 0.24198 + 0.28839i
60 0.18823 + 0.32603i
70 0.12876 + 0.35376i
80 0.065372 + 0.37074i
90 0 + 0.37646i
100 -0.065372 + 0.37074i
110 -0.12876 + 0.35376i
120 -0.18823 + 0.32603i
130 -0.24198 + 0.28839i
140 -0.28839 + 0.24198i
150 -0.32603 + 0.18823i
160 -0.35376 + 0.12876i
170 -0.37074 + 0.065372i
180 -0.37646 + 0i
where $y = y(x)$ is complex valued function.
The exact solution of the derivative is shown below
x dy/dx (exact)
===============================
0 0.082825 + 0i
10 0.078016 + 0.028003i
20 0.064084 + 0.052865i
30 0.042495 + 0.071717i
40 0.015602 + 0.08225i
50 -0.013527 + 0.083005i
60 -0.041391 + 0.073629i
70 -0.064467 + 0.05504i
80 -0.079708 + 0.029423i
90 -0.085034 + 5.2068e-18i
100 -0.079708 - 0.029423i
110 -0.064467 - 0.05504i
120 -0.041391 - 0.073629i
130 -0.013527 - 0.083005i
140 0.015602 - 0.08225i
150 0.042495 - 0.071717i
160 0.064084 - 0.052865i
170 0.078016 - 0.028003i
180 0.082825 - 1.0143e-17i
Can someone help me match the numerical derivative to the exact solution?