<iframe 
    src="https://jsxgraph.uni-bayreuth.de/share/iframe/3d-function-graph-with-gradient-plane" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: 3D function graph with gradient plane" 
    allowfullscreen
></iframe>

<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    var board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-8, 8, 8, -8],
        keepaspectratio: false,
        axis: false
    });
    
    var box = [-5, 5];
    var view = board.create('view3d',
        [
            [-6, -3],
            [8, 8],
            [box, box, box]
        ], {
            xPlaneRear: {
                visible: false
            },
            yPlaneRear: {
                visible: false
            },
        });
    
    // Slider to manipulate the function F below.
    var s = board.create('slider', [[-7, -6], [5, -6], [-3, 0.3, 4]], {name: 's'});
    
    // Function F to be plotted
    var F = (x, y) => s.Value() * x * y + 2;
    
    // 3D surface
    var c = view.create('functiongraph3d', [F, box, box], {
        strokeWidth: 0.5,
        stepsU: 70,
        stepsV: 70
    });
    
    // 3D point: point on xy plane
    var Axy = view.create('point3d', [2, 2, -5], {
        withLabel: false,
        size: 5
    });
    
    // Project Axy to the surface
    var A = view.create('point3d', [
       () => [Axy.X(), Axy.Y(), F(Axy.X(), Axy.Y())]
    ], {
        withLabel: false
    });
    view.create('line3d', [Axy, A], {
        dash: 1
    });
    
    // Hard coded, partial derivatives of F in point A
    var dFx = () => s.Value() * A.Y(),
        dFy = () => s.Value() * A.X(),
        dFx_vec = [1, 0, dFx],
        dFy_vec = [0, 1, dFy];
    
    // Gradient plane
    var plane1 = view.create('plane3d', [A, dFx_vec, dFy_vec, [() => -dFx(), dFx], [() => -dFy(), dFy]], {
        fillOpacity: 0.8,
        fillColor: 'red'
    });
    var a = view.create('line3d', [A, dFx_vec, [0, dFx]]);
    var b = view.create('line3d', [A, dFy_vec, [0, dFy]]);
 </script> 

<jsxgraph width="100%" aspect-ratio="1 / 1" title="3D function graph with gradient plane" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   var board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-8, 8, 8, -8],
       keepaspectratio: false,
       axis: false
   });
   
   var box = [-5, 5];
   var view = board.create('view3d',
       [
           [-6, -3],
           [8, 8],
           [box, box, box]
       ], {
           xPlaneRear: {
               visible: false
           },
           yPlaneRear: {
               visible: false
           },
       });
   
   // Slider to manipulate the function F below.
   var s = board.create('slider', [[-7, -6], [5, -6], [-3, 0.3, 4]], {name: 's'});
   
   // Function F to be plotted
   var F = (x, y) => s.Value() * x * y + 2;
   
   // 3D surface
   var c = view.create('functiongraph3d', [F, box, box], {
       strokeWidth: 0.5,
       stepsU: 70,
       stepsV: 70
   });
   
   // 3D point: point on xy plane
   var Axy = view.create('point3d', [2, 2, -5], {
       withLabel: false,
       size: 5
   });
   
   // Project Axy to the surface
   var A = view.create('point3d', [
      () => [Axy.X(), Axy.Y(), F(Axy.X(), Axy.Y())]
   ], {
       withLabel: false
   });
   view.create('line3d', [Axy, A], {
       dash: 1
   });
   
   // Hard coded, partial derivatives of F in point A
   var dFx = () => s.Value() * A.Y(),
       dFy = () => s.Value() * A.X(),
       dFx_vec = [1, 0, dFx],
       dFy_vec = [0, 1, dFy];
   
   // Gradient plane
   var plane1 = view.create('plane3d', [A, dFx_vec, dFy_vec, [() => -dFx(), dFx], [() => -dFy(), dFy]], {
       fillOpacity: 0.8,
       fillColor: 'red'
   });
   var a = view.create('line3d', [A, dFx_vec, [0, dFx]]);
   var b = view.create('line3d', [A, dFy_vec, [0, dFy]]);
</jsxgraph>