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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

withStudent[MultivariateCalculus]:

DirectionalDerivativex2+y2,x,y=1,2,3,4

225

(1)

DirectionalDerivativex2+y2,x,y=4,4,4,4,output=animation,frames=7

The command to create the plot from the Plotting Guide is

DirectionalDerivativex2+y2,x,y=4,4,6,6,x=8..2,y=0..6,z=0..40,output=plot

See Also

Physics[Vectors][DirectionalDiff], plot3d/options, Student, Student[MultivariateCalculus], Student[MultivariateCalculus][DirectionalDerivativeTutor], tensor[directional_diff], VectorCalculus[DirectionalDiff]


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