Diferencial de uma função

Uma função ${\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} ^{m}}$ se diz diferenciável no ponto ${\displaystyle a\in \mathbb {R} ^{n}}$ se existe uma aplicação linear ${\displaystyle \ell$ :\mathbb {R} ^{n}\to \mathbb {R} ^{m}} tal que:

${\displaystyle \lim _{x\to a}{\dfrac {f(x)-f(a)-\ell (x-a)}{||x-a||}}=0.}$

Em tal caso, ${\displaystyle \ell =\ell (a)}$ denota-se ${\displaystyle Df(a)}$ e se denomina a diferencial da função ${\displaystyle f}$ no ponto ${\displaystyle a.}$

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• Diferencial de uma funçãono projeto Wolfram Demonstrations