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Student[MultivariateCalculus][Gradient] - return the gradient at specified points
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Calling Sequence
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Gradient(f(x,y,..), [x,y,..]=[a1,b1,..], x=xmin..xmax, y=ymin..ymax, ..., opts)
Gradient(f(x,y,..), [x,y,..]=[[a1,b1,..],[a2,b2,..],..], x=xmin..xmax, y=ymin..ymax, ..., opts)
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Parameters
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f(x, y, ..)
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algebraic expression
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x, y, ..
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name; independent variables
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[a1, b1, ..]
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list or list of lists of real constants or names; point(s) at which the gradient is evaluated
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xmin, xmax, ymin, ymax, ...
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(optional) real constants specifying range over which to plot function
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opts
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(optional) equation(s) of the form option=value where option is one of functionoptions, gradientoptions, gradplotoptions, output, or showfunction; specify output options
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Description
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The Gradient(f(x, y,...), [x, y,...] = [a1, b1,...]) calling sequence returns the gradient of the function f at specified points. Multiple points can be given by putting them into a list, for example, Gradient(f(x,y), [x,y] = [[1,2],[2,0]]). In the case of a function of 2 variables, the output option can be used to request that a plot or gradplot be returned.
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If the output=plot is given (so in particular, the function expression has at most two variables), the opts argument can be used to control the appearance of the plot.
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Specifies the plot or gradplot caption. The default caption is constructed from the parameters.
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Specifies the plot options for plotting the function  . For more information on plotting options, see plot3d/options.
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Specifies the plot options for plotting the gradient of the function. For more information on plotting options, see plot3d/options.
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output = value, plot, or gradplot
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This option controls the return value of the function.
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* output = value specifies that the value of the gradient is to be returned. Plot options are ignored if output = value. The default is output = value.
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* output = plot specifies that a plot displays, which shows the function, a level curve at the point, the projection of that level curve onto the x-y plane, and a scaled vector in the direction of the gradient.
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*  specifies that a gradplot displays.
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Specifies the plot options if the output is a gradplot. For more information on plotting options, see plot/options.
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showfunction = true or false
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Determines whether the function  is plotted. The default is true.
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Specifies the plot or gradplot title. If output = gradplot, the default is The Gradient Field. For more information on typesetting the caption, see plot/typesetting.
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The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption , see plot/typesetting.
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The default title is constructed from the parameters and the command options. title = "" disables the default title. For more information about specifying a title, see plot/typesetting.
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For information on how to change the default colors, see the Student[SetColors] help page.
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Examples
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![with(Student[MultivariateCalculus])](/support/helpjp/helpview.aspx?si=3961/file05045/math282.png)
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![Gradient(x^2+y^2, [x, y] = [0, 1])](/support/helpjp/helpview.aspx?si=3961/file05045/math286.png)
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]](/support/helpjp/helpview.aspx?si=3961/file05045/math289.png)
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![Gradient(x^2+y^2, [x, y] = [[0, 1], [2, 1]])](/support/helpjp/helpview.aspx?si=3961/file05045/math293.png)
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, Vector[column]([[4], [2]])]](/support/helpjp/helpview.aspx?si=3961/file05045/math296.png)
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![Gradient(x^2+y^2, [x, y] = [[0, 1], [2, 1]], output = gradplot)](/support/helpjp/helpview.aspx?si=3961/file05045/math300.png)
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The command to create the plot from the Plotting Guide is
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![Gradient(x^2+y^2, [x, y] = [[0, 1], [2, 1]], x = -2 .. 5, y = -2 .. 5, z = 0 .. 10, output = plot)](/support/helpjp/helpview.aspx?si=3961/file05045/math314.png)
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