Using Two point Forward difference, Backward difference, Central difference formula numerical differentiation to find solution

x	1	1.05	1.10	1.15	1.20	1.25	1.30
f(x)	1	1.02470	1.04881	1.07238	1.09545	1.11803	1.14018

`f^'(1.15) and f^('')(1.15)`

Solution:
The value of table for `x` and `y`

x	1	1.05	1.1	1.15	1.2	1.25	1.3
y	1	1.0247	1.0488	1.0724	1.0954	1.118	1.1402

Two-point FDF (Forward difference formula)
`f^'(x)=(f(x+h)-f(x))/h`

`f^'(1.15)=(f(1.15+0.05)-f(1.15))/0.05`

`f^'(1.15)=(f(1.2)-f(1.15))/0.05`

`f^'(1.15)=(1.0954-1.0724)/0.05`

`f^'(1.15)=0.4614`

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Two-point BDF (Backward difference formula)
`f^'(x)=(f(x)-f(x-h))/h`

`f^'(1.15)=(f(1.15)-f(1.15-0.05))/0.05`

`f^'(1.15)=(f(1.15)-f(1.1))/0.05`

`f^'(1.15)=(1.0724-1.0488)/0.05`

`f^'(1.15)=0.4714`

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Two-point CDF (Central difference formula)
`f^'(x)=(f(x+h)-f(x-h))/(2h)`

`f^'(1.15)=(f(1.15+0.05)-f(1.15-0.05))/(2*0.05)`

`f^'(1.15)=(f(1.2)-f(1.1))/0.1`

`f^'(1.15)=(1.0954-1.0488)/0.1`

`f^'(1.15)=0.4664`

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