Linear Approximation 3d

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\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{math}
\usepackage{ifthen}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
% File name: linear-approximation-3d.tex
% Description: 
% The linear approximation for a function of two variables $z = f(x,y)$ is shown.
% 
% Date of creation: March, 7th, 2021.
% Date of last modification: October, 9th, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Source: page 15 of the 
% Glosario Ilustrado de Matem\'aticas Escolares.
% https://tinyurl.com/5udm2ufy
%
% Terms of use:
% According to TikZ.net
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% Your commitment to the terms of use is greatly appreciated.
%
\begin{document}
%
\tdplotsetmaincoords{70}{130}
%
\begin{tikzpicture}[tdplot_main_coords]
    % functions
    \tikzmath{function funcion(\x,\y) {return (\x*\x+3*\y*\y)*e^(-\x*\x-\y*\y);};} % the function $z = f(x,y)$
    \tikzmath{function derivadax(\x,\y) {return -2.0*\x*(-1.0 + \x * \x + 3.0 * \y * \y) * exp(-\x*\x - \y*\y);};}  % $f_{x}$
    \tikzmath{function derivaday(\x,\y) {return -2.0*\y*(-3.0 + \x * \x + 3.0 * \y * \y) * exp(-\x*\x - \y*\y);};}  % $f_{y}$
    % equation of the plane
    \tikzmath{function plano(\x,\y) {return derivadax(\xcero,\ycero)*(\x-\xcero)+derivaday(\xcero,\ycero)*(\y-\ycero)+\zcero;};}
    %   
    \pgfmathsetmacro{\dominio}{0.75*pi} % domain for plotting
    \pgfmathsetmacro{\step}{\dominio/50.0} % step size
    \pgfmathsetmacro{\max}{\dominio}
 
 
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