Difference between revisions of "Strong derivative/Infobox"

	Strong derivative
	lim; 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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 {{Infobox
 |title=Strong derivative
-|above=<span style="font-size:1.25em;">{{MM|1=\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} }}</span><br/>For two [[normed space|normed spaces]] {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}} and a [[mapping]] {{M|T:U\rightarrow Y}} for {{M|U}} some [[open set]] in {{M|X}}
+|above=<span style="font-size:1.25em;">{{MM|1=\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)}}</span><br/>For two [[normed space|normed spaces]] {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}}<br/>and a [[mapping]] {{M|f:U\rightarrow Y}} for {{M|U}} [[open set|open]] in {{M|X}}<br/><br/>{{M|df\vert_{x_0}:X\rightarrow Y}} a [[linear map]] called the<br/>"''derivative of {{M|f}} at {{M|x_0}}''"
 }}<noinclude>
 {{Stub page|This is just a stub, CHECK THE INFOBOX DEFINITION IS VALID}}
 [[Category:Infoboxes]]
 </noinclude>

Strong derivative
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 $x_0$ "