# Questions tagged [frechet-derivative]

The Fréchet derivative of a function from an open subset of a Banach space into another Banach space at a point is a linear map from the first Banach space into the second one which approximates particularly well the function near the given point. It generalizes the concept of derivative of a real function of one real variable.

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### Fréchet derivative with composition of norm

I'm trying to understand an argument to compute a Fréchet derivative. Someone could help me to figure out? I don't see where it comes from the 2nd equality. The first one it's only use the identity ...
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### Is there a sense in which a function converges to its total derivative?

In short: Is there a way to rigorously define the total derivative (of $F$ at $x$) as a function $dF_x$ which is (1) linear and (2) a usual topological limit of some function $\mu:X\to Y$, where $X$ ...
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### Chain rule and generalized composition of multilinear maps

I know that if functions $f : \mathbb{R}^n \to \mathbb{R}^m$ and $g : \mathbb{R}^m \to \mathbb{R}^p$ are differentiable at $x \in \mathbb{R}^n$ and $f(x) \in \mathbb{R}^m$, respectively, with ...
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Let $F$ be a Hilbert space and $\Theta$ a $d$-dimensional closed Riemannian manifold. Consider the twice Fréchet differentiable functions $R \colon F \to [0, \infty)$ and $\phi \colon \Theta \to F$ ...