directional derivative

[də′rek·shən·əl də′riv·əd·iv] (mathematics) The rate of change of a function in a given direction; more precisely, if ƒ maps an n-dimensional euclidean space into the real numbers, andx= (x₁, …, x_n) is a vector in this space, andu= (u₁, …, u_n) is a unit vector in the space (that is, u₁²+···+ u_n ²= 1), then the directional derivative of ƒ atxin the direction ofuis the limit as h approaches zero of [ƒ(x+ h u) - ƒ(x)]/ h.

单词	directional derivative
释义	directional derivative directional derivative [də′rek·shən·əl də′riv·əd·iv] (mathematics) The rate of change of a function in a given direction; more precisely, if ƒ maps an n-dimensional euclidean space into the real numbers, andx= (x₁, …, x_n) is a vector in this space, andu= (u₁, …, u_n) is a unit vector in the space (that is, u₁²+···+ u_n ²= 1), then the directional derivative of ƒ atxin the direction ofuis the limit as h approaches zero of [ƒ(x+ h u) - ƒ(x)]/ h.
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