Hello,

I'm having "big" issue recalling formula for numerical differentiation... using front differences $\displaystyle (y[n+1]-y[n])$... and can't find any of my old textbooks... so if anyone could guide me a little bit, i would be very grateful

let's say i have function given like :

and i need to get formula for numerical differentiation using front differences (or back)... and get approximate value of derivate at point x=-2....

x _{i}-2 -1 0 1 2 f(x _{i})-3 -1 0 -1 0

well...

i assume this...

$\displaystyle f'(x) = \frac{f(x)}{x[i+1]- x[i]} $

it's probably wrong, but even if it's correct i don't know what to do next ... because I think need only two points from this table to determine the value of the derivate?

P.S. i don't see why do i get latex error

edit:

or i have to use table of front differences ?

$\displaystyle y_1$ $\displaystyle \Delta y_1$ $\displaystyle y_2$ $\displaystyle \Delta^2 y_1$ $\displaystyle \Delta y_2$ $\displaystyle \Delta^3 y_1$ $\displaystyle y_3$ $\displaystyle \Delta^2 y_2$ $\displaystyle \Delta^4 y_1$ $\displaystyle \Delta y_3$ $\displaystyle \Delta^3 y_2$ $\displaystyle y_4$ $\displaystyle \Delta^2 y_3$ $\displaystyle \Delta y_4$ $\displaystyle y_5$