In numerical analysis

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

, numerical differentiation describes algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

s for estimating the derivative

Derivative

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

 of a mathematical function or function subroutine

Subroutine

In computer science, a subroutine is a portion of code within a larger program that performs a specific task and is relatively independent of the remaining code....

 using values of the function and perhaps other knowledge about the function.


The simplest method is to use finite difference approximations.

A simple two-point estimation is to compute the slope of a nearby secant line

Secant line

A secant line of a curve is a line that intersects two points on the curve. The word secant comes from the Latin secare, to cut.It can be used to approximate the tangent to a curve, at some point P...

 through the points (x,f(x)) and (x+h,f(x+h)).