Solving a Nonlinear Equation using Newton-Raphson Method

I tried making codes that solving a nonlinear equ using Newton-Raphson method but there is an error that 'Index exceeds the number of array elements. Index must not exceed 1.' at line 3 'df1dx1 = (u(x(1)+del*x(1),x(2))-u(x(1),x(2)))/(del*x(1)); ' But Idk why there's an error and how to fix it. I think I did well. how to fix it? There's my code below

function [J,f]=jfreact(x)

del = 0.000001;

df1dx1 = (u(x(1)+del*x(1),x(2))-u(x(1),x(2)))/(del*x(1));

df1dx2 = (u(x(1),x(2)+del*x(2))-u(x(1),x(2)))/(del*x(2));

df2dx1 = (v(x(1)+del*x(1),x(2))-v(x(1),x(2)))/(del*x(1));

df2dx2 = (v(x(1),x(2)+del*x(2))-v(x(1),x(2)))/(del*x(2));

J=[df1dx1 df1dx2; df2dx1 df2dx2];

f1=u(x(1),x(2));

f2=v(x(1),x(2));

f=[f1;f2];

end

function f = u(x,y)

f = y+x^2-x-0.75;

end

function f = v(x,y)

f = y+5*x*y-x^2;

end

--------------From here, this is a code that find the roots (initial values are all zeros, iteration is 3)

clear;clc;

format short e;

x=[0;0];

for i=1:3

[J,f]=jfreact(x);

x=x-J\f;

end

------------I'd like to know how to run well.... Please help me...

Answer 1

[Torsten]

x=[0;0];
for i=1:3
  [J,f]=jfreact(x);
  x=x-J\f
end

function [J,f]=jfreact(x)
  del = 0.000001;
  df1dx1 = (u(x(1)+del,x(2))-u(x(1),x(2)))/del;
  df1dx2 = (u(x(1),x(2)+del)-u(x(1),x(2)))/del;
  df2dx1 = (v(x(1)+del,x(2))-v(x(1),x(2)))/del;
  df2dx2 = (v(x(1),x(2)+del)-v(x(1),x(2)))/del;
  J=[df1dx1 df1dx2; df2dx1 df2dx2];
  f1=u(x(1),x(2));
  f2=v(x(1),x(2));
  f=[f1;f2];
end
function f = u(x,y)
  f = y+x^2-x-0.75;
end
function f = v(x,y)
  f = y+5*x*y-x^2;
end

[민석 최]

thanks a lot