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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)




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



list(name); a list of the form [x1, x2, ..., xn] specifying the n independent variables of f



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



list(realcons) or list(name); a list of values representing the direction vector with which the directional derivative is evaluated



(optional) equation of the form x1=x1_min..x1_max, where x1 is a variable given in vars



(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



(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)



(optional) equation(s) of the form option=value; these equations specify the output options; please see the Options section for details



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.







The command to create the plot from the Plotting Guide is


See Also

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

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