Combined derivative and smoothing

Central difference First Derivatives:

First Derivative with one 3-point triangular smooth
-0.25	-0.5	0	0.5	0.25

First Derivative with one 5-point triangular smooth
-0.1111111111	-0.2222222222	-0.2222222222	0	0.2222222222	0.2222222222	0.1111111111

First Derivative with one 7-point triangular smooth
-0.0625	-0.125	-0.125	-0.125	0	0.125	0.125	0.125	0.0625

First Derivative with one 9-point triangular smooth
-0.04	-0.08	-0.08	-0.08	-0.08	0	0.08	0.08	0.08	0.08	0.04

First Derivative with one 11-point triangular smooth
-0.0277777778	-0.0555555556	-0.0555555556	-0.0555555556	-0.0555555556	-0.0555555556	0	0.0555555556	0.0555555556	0.0555555556	0.0555555556	0.0555555556	0.0277777778

First Derivative with one 13-point triangular smooth
-0.0204081633	-0.0408163265	-0.0408163265	-0.0408163265	-0.0408163265	-0.0408163265	-0.0408163265	0	0.0408163265	0.0408163265	0.0408163265	0.0408163265	0.0408163265	0.0408163265	0.0204081633

First Derivative with one 15-point Gaussian smooth
1	4	9	16	21	20	13	0	-13	-20	-21	-16	-9	-4	-1

First Derivative with two 3-point triangular smooths
-0.0625	-0.25	-0.3125	0	0.3125	0.25	0.0625

First Derivative with two 5-point triangular smooths
-0.012345679	-0.049382716	-0.1111111111	-0.1481481481	-0.1111111111	0	0.1111111111	0.1481481481	0.1111111111	0.049382716	0.012345679

First Derivative with two 7-point triangular smooths
-0.00390625	-0.015625	-0.03515625	-0.0625	-0.08203125	-0.078125	-0.05078125	0	0.05078125	0.078125	0.08203125	0.0625	0.03515625	0.015625	0.00390625
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Second Derivatives:

Second Derivative with two 7-point triangular smooths
0.00390625	0.0078125	0.01171875	0.015625	0.00390625	-0.0078125	-0.01953125	-0.03125	-0.01953125	-0.0078125	0.00390625	0.015625	0.01171875	0.0078125	0.00390625

Second Derivative with two 9-point triangular smooths = 19 coefficients
0.0016	0.0032	0.0048	0.0064	0.008	0.0032	-0.0016	-0.0064	-0.0112	-0.016	-0.0112	-0.0064	-0.0016	0.0032	0.008	0.0064	0.0048	0.0032	0.0016

Second Derivative with a 15-point Gaussian smooth
1	4	10	14	11	-4	-21	-30	-21	-4	11	14	10	4	1

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Central-difference Third Derivative with 17-point Gaussian smooth
1	4	9	10	1	-18	-32	-26	0	26	32	18	-1	-10	-9	-4	-1

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Fourth Derivative with 17-point Triangular smooth
1	2	3	-2	-7	-12	-2	8	18	8	-2	-12	-7	-2	3	2	1