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In multivariable calculus, the directional derivative measures the rate at which a function changes in a particular direction at a given point. [citation needed]The directional derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a direction ...
The function atan2(y, x) can be used instead of the mathematical function arctan(y/x) owing to its domain and image. ... Directional derivative (A ⋅ ∇)B [3] ...
where i, j, k are the standard unit vectors for the x, y, z-axes. More generally, for a function of n variables ... is the directional derivative in the direction of ...
The directional derivative of a scalar function f(x) ... the derivative of a vector function y with respect to a vector x whose components represent a space is known ...
The directional derivative of a scalar field (,,) in the direction (,,) = ^ + ^ + ^ ... The 3 remaining vector derivatives are related by the equation:
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
The original theorem given by J. M. Danskin in his 1967 monograph [1] provides a formula for the directional derivative of the maximum of a (not necessarily convex) directionally differentiable function. An extension to more general conditions was proven 1971 by Dimitri Bertsekas.
The directional derivative of in the direction is defined by = (+) if the limit exists. One says that F {\displaystyle F} is continuously differentiable, or C 1 {\displaystyle C^{1}} if the limit exists for all v ∈ X {\displaystyle v\in X} and the mapping D F : U × X → Y {\displaystyle DF:U\times X\to Y} is a continuous map.