compute the directional derivative - Maple Help

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Student[MultivariateCalculus][DirectionalDerivative] - compute the directional derivative

 Calling Sequence DirectionalDerivative(f, vars, dir, r1, r2, r3, opts) DirectionalDerivative(f, vars=pt, dir, r1, r2, r3, opts)

Parameters

 f - algebraic, list(algebraic), or Vector(algebraic); a function in n-variables; this function can be vector-valued, in which case it must be a list or a Vector of its component functions vars - list(name); a list of the form [x1, x2, ..., xn] specifying the n independent variables of f pt - list(name) or list(realcons); a list of values representing the point at which the directional derivative is evaluated; the dimension of this point must be the same as the number of variables specified in var dir - list(realcons) or list(name); a list of values representing the direction vector with which the directional derivative is evaluated r1 - (optional) equation of the form x1=x1_min..x1_max, where x1 is a variable given in vars r2 - (optional) equation of the form x2=x2_min..x2_max, where x2 is a variable given in vars; together with r1, r2 specifies the plot or animation ranges for the independent variables specified in vars; note that plotting and animating are only available if f is a real-valued (scalar) function of two variables r3 - (optional) equation of the form z=z_min..z_max, where z is any name not in vars; this range specifies the plotting or animation range for the dependent variable (the z-axis) opts - (optional) equation(s) of the form option=value; these equations specify the output options; please see the Options section for details

Description

 • The DirectionalDerivative command returns the directional derivative  of f, evaluated at pt if it is specified, in the direction given by dir; that is, the product of the Jacobian  matrix of the function f, evaluated at pt if it is specified, and the normalized direction vector dir.
 • In particular, if f is a real-valued (scalar) function, then this command returns the dot product of the gradient of f and the normalized direction vector dir, which is a scalar.
 • If the output option in opts is specified to be plot or animation, the command returns a plot of the directional derivative or an animation of the directional derivative in various directions, respectively. Otherwise, by default, the output is the computed value of the directional derivative.
 • The DirectionalDerivativeTutor routine offers equivalent capabilities to DirectionalDerivative in a tutor interface. See the Student[MultivariateCalculus][DirectionalDerivativeTutor] help page.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{MultivariateCalculus}]\right):$
 > $\mathrm{DirectionalDerivative}\left({x}^{2}+{y}^{2},\left[x,y\right]=\left[1,2\right],\left[3,4\right]\right)$
 $\frac{{22}}{{5}}$ (1)
 > $\mathrm{DirectionalDerivative}\left({x}^{2}+{y}^{2},\left[x,y\right]=\left[-4,4\right],\left[-4,4\right],\mathrm{output}=\mathrm{animation},\mathrm{frames}=7\right)$

The command to create the plot from the Plotting Guide is

 > $\mathrm{DirectionalDerivative}\left({x}^{2}+{y}^{2},\left[x,y\right]=\left[-4,4\right],\left[-6,-6\right],x=-8..-2,y=0..6,z=0..40,\mathrm{output}=\mathrm{plot}\right)$