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frechet_derivative_chain_rule [2013/09/15 20:26]
nikolaj
frechet_derivative_chain_rule [2014/03/21 11:11] (current)
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 ===== Fréchet derivative chain rule ===== ===== Fréchet derivative chain rule =====
 ==== Theorem ==== ==== Theorem ====
-| @#88DDEE: $X,Y,Z$ ... Banach spaces with topology | +| @#55CCEE: context ​    | @#55CCEE: $X,Y,Z$ ... Banach spaces with topology | 
-| @#88DDEE: $f\in C(X,Y)$ | +| @#55CCEE: context ​    | @#55CCEE: $f\in C(X,Y)$ | 
-| @#88DDEE: $g\in C(Y,Z)$ |+| @#55CCEE: context ​    | @#55CCEE: $g\in C(Y,Z)$ |
  
-| @#55EE55: $ D(g\circ f)=(Dg)\circ f\ \cdot\ Df $ |+| @#55EE55: postulate ​  | @#55EE55: $ D(g\circ f)=(Dg)\circ f\ \cdot\ Df $ |
  
 where $\circ$ denotes the concatenation of functions of $X,Y$, which is taken to bind stronger than the concatenation $\cdot$ of linear operators. where $\circ$ denotes the concatenation of functions of $X,Y$, which is taken to bind stronger than the concatenation $\cdot$ of linear operators.
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 Wikipedia: [[http://​en.wikipedia.org/​wiki/​Chain_rule|Chain rule]], [[http://​en.wikipedia.org/​wiki/​Chain_rule_%28disambiguation%29|Chain rule (disambiguation)]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Chain_rule|Chain rule]], [[http://​en.wikipedia.org/​wiki/​Chain_rule_%28disambiguation%29|Chain rule (disambiguation)]]
 ==== Parents ==== ==== Parents ====
-=== Requirements ​===+=== Context ​===
 [[Fréchet derivative]] [[Fréchet derivative]]
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