We can use forward, backward or central difference formula to calculate the partial derivatives of a 1D (x) or 2D (x,y) function. What will be the formula using any of the methods to calculate the derivative of a 3D (x,y,z) function?
Like for 2D (x,y) function, the forward difference formula is -
I suppose that by 2D central differentiation formula you mean:
$f_x(x,y)=$lim$_{h\to 0}\frac{f(x+h/2,y)-f(x-h/2,y)}{h}.$
Now, for 3D functions there are no differences:
$f_x(x,y,z)=$lim$_{h\to 0}\frac{f(x+h/2,y,z)-f(x-h/2,y,z)}{h},$ and likewise for $f_y$ and $f_z.$
If you have other questions ask me, I don't know if this was your doubt precisely, maybe you were asking a different thing.