INPUT: f(x) on domain[0,L], N:integer, L; integer
OUTPUT: f'(x)=g[1,2,...,N]

start
define dx = L/N.
for i = 0 : N do
	x[i] i x dx,
	fx[i] = f(xi)
endfor
	for i = 0 : N -1 do
	gx[i] = (fx[i+1]-fx[i]) / deltaX
	OUTPUT" gx[i]"
endfor
gx[N] = (fx[N] - fx[N-1]) / deltaX  // use backward on boundary
OUTPUT" gx[N]"
end