Directional Derivative
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In mathematics, the directional derivative of a multivariate differentiable function along a given vector (mathematics)|vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the Curvilinear coordinates|coordinate curves, all other coordinates being constant. The directional derivative is a special case of the Gâteaux derivative.
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