# Partial derivatives of a 3D function formula

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 -

• Where's the "centering" in the above definition? – Riccardo Ceccon Mar 21 '18 at 17:21
• My bad. It is forward difference formula. I corrected it. @RiccardoCeccon – user3503711 Mar 21 '18 at 17:37

$f_x(x,y)=$lim$_{h\to 0}\frac{f(x+h/2,y)-f(x-h/2,y)}{h}.$
$f_x(x,y,z)=$lim$_{h\to 0}\frac{f(x+h/2,y,z)-f(x-h/2,y,z)}{h},$ and likewise for $f_y$ and $f_z.$