I have found the derivatives wrt to x and y using the central difference formula below:

Code:

f=@(x,y)2*x^2*y+3*x*y^3;%function_handle
h = 1e-10;%step size
xi = 2;%Point to evaluate function
yi = 1;
% Estimate derrivatives by central difference method
dfdx = (f(xi+h,yi)-f(xi-h,yi))/(2*h)
dfdy = (f(xi,yi+h)-f(xi,yi-h))/(2*h)

Result from after running (MATLAB command prompt)

Code:

dfdx =
11.0000
dfdy =
26.0000
EDU>>

Can I use these values to find the value of $\displaystyle \frac{{{\partial }^{2}}f(x,y)}{\partial x\partial y}$ at this point?

Regards Elbarto