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名詞

directional derivative (plural directional derivatives)

1. (calculus) A function which measures the rate of change of some other function at any point in a particular direction; formally, the directional derivative of a scalar function ${\\displaystyle f(\\mathbf {x} )=f(x_{1},x_{2},\\ldots ,x_{n})}$ along a vector ${\\displaystyle \\mathbf {v} =(v_{1},\\ldots ,v_{n})}$ is the function ${\\displaystyle \\nabla _{\\mathbf {v} }{f}}$ defined by the limit ${\\displaystyle \\nabla _{\\mathbf {v} }{f}(\\mathbf {x} )=\\lim _{h\\to 0}{\\frac {f(\\mathbf {x} +h\\mathbf {v} )-f(\\mathbf {x} )}{h}}}$.