How to calculate limit in n-number of times?

Hi guys, I am working on a function which can generate the differentiation of equation given as input.

But I am trying to make it automatically given answer as input k. if k=1, then it will give the first differentiation, and so on.

and so I put dx^k on my code below, but matlab replied me with limit should be variable only. do you guys have any idea how to make it automatic?

function [Y_1,Y_2]=PolynomialDifferentiation (A,k)
syms x dx
Equation=poly2sym(A)
i=numel(A)
k=1:i-1
Equation_1=subs(Equation,x,(x+dx)); %to calculate F(x+dx)
Y=(Equation_1-Equation)/dx %(F(x+dx)-F(x))/dx
firstDiff=limit(Y,dx,0)%to define first differentiation of given equation
answer=coeffs(firstDiff)

secondEquation=firstDiff
C_1=subs(firstDiff,x,(x+dx));
D=(C_1-firstDiff)/dx;
secondDiff=limit(D,dx,0)
answer=coeffs(secondDiff)

Answer 1

[Matt J]

I can't quite understand what your code is trying to do, but if you are trying to get the k-th derivative of a polynomial, given its coefficients A, you could just do

for i=1:k
    A=polyder(A);
end

[Yanuar Rizki Pahlevi]

Hi, thank you for your response. Yes, i know i can use polyder, but I am trying to not use any polynomial equation at all.