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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

 X Y 1.4 1.6 1.8 2 2.2 4.0552 4.953 6.0496 7.3891 9.025

Newton's forward differentiation table is as follows.
 X Y(X) DeltaY Delta^2Y Delta^3Y Delta^4Y 1.4 4.0552 0.8978 1.6 4.953 0.1988 1.0966 0.0441 1.8 6.0496 0.2429 0.0094 1.3395 0.0535 2 7.3891 0.2964 1.6359 2.2 9.025

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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