backward-difference formula

Approximating a derivative from the current point and one point behind it.

The backward-difference formula approximates $f'(x)$ by $\dfrac{f(x)-f(x-h)}{h}$ , the slope of the secant line through $(x-h,f(x-h))$ and $(x,f(x))$ . Like the forward-difference formula, its truncation error is $O(h)$ .

Examples

At the RIGHT endpoint of a data table, only the backward-difference formula is usable -- there's no $f(x+h)$ value available to build the forward version.