Concept

# Numerical differentiation

Summary
In numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function. Finite differences The simplest method is to use finite difference approximations. A simple two-point estimation is to compute the slope of a nearby secant line through the points (x, f(x)) and (x + h, f(x + h)). Choosing a small number h, h represents a small change in x, and it can be either positive or negative. The slope of this line is : \frac{f(x + h) - f(x)}{h}. This expression is Newton's difference quotient (also known as a first-order divided difference). The slope of this secant line differs from the slope of the tangent line by an amount that is approximately proportional to h. As h approaches zero, the slope of the secant line approaches the slope of the tangent line. Therefore, the true derivative of f at x is the limit of the value
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