Calculate derivative with 3 matrices

Hello. Given 3 matrices, X, Y and Z, how can I approximate the derivative on Z on a given point (x, y) ?

I'm not supposed to use the gradient function.

Any help highly appreciated.

Answer 1

[dbmn]

What would you do if you only had 1 Dimension?

You would do (y2-y1)/(x2-x1) with x2 being the nearest x to x1. Do exactly the same with multiple Dimensions.

• Any given Point (x,y) will be on/within a triangle of neighboring points A, B, C.
• Find the Points A B C of that triangle and then identify the gradient (hint: normal vector gets you there) in 3D of the area ABC.