# Algorithm To Find Derivatives Using Newtons Backward Difference Formula

## Algorithm

Following steps are required inorder to find derivatives using backward difference formula:

```1. Start

2. Read number of data (n)

3. Read data points for x and y:

For i = 0 to n-1
Next i

4. Read calculation point where derivative is required (xp)

5. Set variable flag to 0

6. Check whether given point is valid data point or not.
If it is valid point then get its position at variable index

For i = 0 to n-1

If |xp - Xi| < 0.0001
index = i
flag = 1
break from loop
End If

Next i

7. If given calculation point (xp) is not in
x-data then terminate the process.

If flag = 0
Print "Invalid Calculation Point"
Exit
End If

8. Generate backward difference table

For i = 1 to n-1

For j = n-1 to i (Step -1)
Yj,i = Yj,i-1 - Yj-1,i-1
Next j

Next i

9. Calculate finite difference: h = X1 - X0

10. Set sum = 0

11. Calculate sum of different terms in formula
to find derivatives using Newton's backward
difference formula:

For  i = 1 to index
term = (Yindex, i)i / i
sum = sum + term
Next i

12. Divide sum by finite difference (h) to get result

first_derivative = sum/h

13. Display value of first_derivative

14. Stop
```