\(To\ be\ able\ to\ use\ Mathematica\ to\ plot\ Gradient\ Vectors\ you\ will\ need\ to\ access\ the\ following\ "Mathematica Package"\ \)
To do this just press the usual Shift - 
      Enter (i . e .  
            execute) the following line :  
Then if you' d like to plot different functions with their gradient vectors,  
    just change the function x^2  -  
      y^2 in the ContourPlot command.

<< Graphics`PlotField`

contour1 = 
        ContourPlot[
          (x^2) - (y^2), {x, -2.2, 2.2}, {y, -2.2, 
            2.2}, 
Contours -> {-4, -3, -2, -1, 0, 1, 2, 3, 4}, ContourShading -> False];

contour2 = 
        PlotGradientField[((x^2) - (y^2)), {x, -2.2, 
            2.2}, {y, -2.2, 2.2}, PlotPoints -> 8];

Show[contour1, contour2];