Comparison between the derivatives of the symbolic function and the interpolated function:
ex = Cos[x];
d = Interpolation[Table[ex, {x, 0 \[Degree], 360 \[Degree], 1 \[Degree]}], InterpolationOrder -> 6];
Plot[{d[t], d'[t]}, {t, 1, 361}]
Plot[{ex, D[ex, x]} // Evaluate, {x, 0 \[Degree], 360 \[Degree]}]
For example for x = 45[Degree]:
The results for the symbolic and interpolated functions are identical:
{Cos[45 \[Degree]], d[46]}
{1/Sqrt[2], 1/Sqrt[2]}
But for derivatives, the results are different. That's it?
{D[ex, x] /. x -> 45 \[Degree], d'[46]} // N
{-0.707107, -0.0123413}
Regards,
Sinval
