Differentiation:

The derivative of a function y = f(x) can be written as follows

or f  '(x) and is defined as the rate of change of the dependent variable y with respect to x. The derivative is the slope of line tangent to the function at given point.

The MATLAB has a function polyder that will find the derivative of a polynomial. For illustration, for the polynomial x³ + 2x² - 4x + 3, that would be represented by the vector

 [1 2 - 4 3], the derivative is found by:

>> origp = [1 2 -4 3];

>> diffp = polyder(origp)

diffp =

3 4 -4

that shows that the derivative is the polynomial 3x² + 4x - 4. The function polyval can be used then to find the derivative for certain values of x; for illustration for x = 1, 2, and 3:

>> polyval(diffp, 1:3)

ans =

3 16 35

The derivative can be written as folows 

and can be approximated by difference equation.