You are not taking a true derivative, but you are calculating the difference between each array element.
Also, you could make your code much more readable by doing something like this:
b0 = diff(yy)/dx;
b1= diff(b)/dx;
b2= diff(b1)/dx;
b3= diff(b2)/dx;
b4= diff(b3)/dx;
b5= diff(b4)/dx;
b6= diff(b5)/dx;
b7= diff(b6)/dx;
By not using numbered variables, but using a cell array instead, you can further simplify the code:
b=cell(1,8);
b{1}=diff(yy)/dx;
y=cell(1,numel(b));
y{1}=sin(a);
y{2}=y{1}+b{1}*(x-a)
for n=2:numel(b)
b{n}=diff(b{n-1})/dx;
y{n+1}=y{n} + b{n}*((x-a)^n)/factorial(n);
end
Note that Matlab is one-indexed, meaning that y0 becomes y{1}.
If you use the symbolic toolbox to generate the variable x, this should work as intended. For a numerical fix, you will have to think about how you want to extend you vector after you apply diff.
