Forward difference gradient vector in multiple dimensions

If I have a function of the form

f = @(x) x.^2

then given a step-size h, I can use a forward difference given by

fd = @(x) (f(x+h)-f(x))/h

to get a rough estimate of its gradient in 1 dimension. However, if I have a 2 dimensional function of the form

f = @(x) x(1).^2 + x(2).^2

how would I go about finding the gradient vector, using forward differences of this function? The gradient for each component would be given by df/dx1 = (f(x1+h,x2)-f(x1,x2))/h and df/dx1 = (f(x1,x2+h)-f(x1,x2))/h, but unfortunately I can't seem to be able to figure out how to code this in MATLAB.

Answer 1

[Jan]

h = 0.005;
f = @(x) x(1).^2 + x(2).^2
dfdx1 = @(x) (f([x(1) + h, x(2)]) - f(x)) / h
dfdx2 = @(x) (f([x(1), x(2) + h]) - f(x)) / h

x = [2,3]
dfdx1(x)
dfdx2(x)