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Problem: Numerical Differentiation, {{1.4,4.0552},{1.6,4.9530},{1.8,6.0496},{2.0,7.3891},{2.2,9.0250}},x=1.4 [ Calculator, Method and examples ]

Solution:
Your problem `->` Numerical Differentiation, {{1.4,4.0552},{1.6,4.9530},{1.8,6.0496},{2.0,7.3891},{2.2,9.0250}},x=1.4


Numerical differentiation method to find solution.
The value of table for `X` and `Y`

X1.41.61.822.2
Y4.05524.9536.04967.38919.025

Newton's forward differentiation table is as follows.
XY(X)`DeltaY``Delta^2Y``Delta^3Y``Delta^4Y`
1.44.0552
0.8978
1.64.9530.1988
1.09660.0441
1.86.04960.24290.0094
1.33950.0535
27.38910.2964
1.6359
2.29.025


The value of `x` at you want to find `f(x) : x_0 = 1.4`

`h = x_1 - x_0 = 1.6 - 1.4 = 0.2`


`[(dy)/(dx)]_(x=x_0) = 1/h * ( Delta Y_0 - 1/2 * Delta^2 Y_0 + 1/3 * Delta^3 Y_0 - 1/4 * Delta^4 Y_0)`






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