derivative_numerical_approximation.sf

#!/usr/bin/ruby

# Numerical approximation of the derivative of a function `f(x)`, at a given value `x`.

# Formula:
#   f'(x) = Limit_{h -> 0} (f(x + h) - f(x))/h

# See also:
#   https://en.wikipedia.org/wiki/Derivative
#   https://en.wikipedia.org/wiki/Numerical_differentiation

func derivative(f, x, h=1e-49) {
    (f(x + h) - f(x)) / h
}

# Example for: f(x) = x^3 + x^2
#       where: f'(x) = 3*x^2 + 2*x

say derivative({|x| x**3 + x**2 }, 10)       #=> 320