Strong derivative/Infobox

Strong derivative

[math]\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)[/math] For two normed spaces [ilmath](X,\Vert\cdot\Vert_X)[/ilmath] and [ilmath](Y,\Vert\cdot\Vert_Y)[/ilmath] and a mapping [ilmath]f:U\rightarrow Y[/ilmath] for [ilmath]U[/ilmath] open in [ilmath]X[/ilmath] [ilmath]df\vert_{x_0}:X\rightarrow Y[/ilmath] a linear map called the "derivative of [ilmath]f[/ilmath] at [ilmath]x_0[/ilmath]"

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