Help with Numerical Differentiation
Prof. Richard B. Goldstein

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JavaScript Syntax

(x2 + 2x - 1)5/3 is Math.pow((x*x+2*x-1),5/3)
eqsample is Math.sqrt(Math.sin(x)/(Math.pow(2,x)+3*Math.log(x)))

calculus formula Javascript Function xo f(1)(xo) f(2) (xo)
#1 x3+2x 1*Math.pow(x,3)+2*x 1 5 6
#2 e3xsin(2x) Math.exp(3*x)*Math.sin(2*x) 0 2 12
The formulas and program will work well for most functions. Note that JavaScript will require the 1 coefficient. This is because it prefers working with strings. That is, y=a+b where a is 2.4 and b is 3.3 will not yield 5.7. Rather, it will get 2.43.3 a value it doesn't understand. Even worse, a = 2.5 and b = 3 will give 2.53 an incorrect number which it does understand. Generally, higher derivatives are less accurate when calculated numerically. The following formulas are basically derived from the Taylor Series approximation of a function.
Formulas:

dffrnteqs

Note that additional points increase the O(hn) of the truncation error. Each level N1, N2,... also increases the order in steps of 2.
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