Strong derivative/Infobox

Strong derivative

$$\lim_{h\rightarrow 0}\left(\frac{T(x_0+h)-T(x_0)}{\Vert h\Vert_X}\right)=\overbrace{L_{x_0}:X\rightarrow Y}^\text{Linear}$$ For two normed spaces $(X,\Vert\cdot\Vert_X)$ and $(Y,\Vert\cdot\Vert_Y)$ and a mapping $T:U\rightarrow Y$ for $U$ some open set in $X$

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