Strong derivative/Infobox

Strong derivative

$$\lim_{h\rightarrow 0}\left(\frac{\big\Vert f(x_0+h)-f(x_0)-df\vert_{x_0}\big\Vert_Y}{\Vert h\Vert_X}\right)$$ For two normed spaces $(X,\Vert\cdot\Vert_X)$ and $(Y,\Vert\cdot\Vert_Y)$ and a mapping $f:U\rightarrow Y$ for $U$ open in $X$ $df\vert_{x_0}:X\rightarrow Y$ a linear map called the "derivative of $f$ at $x_0$"

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