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At a differentiability point, the unique continuous linear map giving the first-order approximation to a function.
This node uses the Fréchet derivative. One-variable derivatives and Jacobian matrices are special presentations; weaker directional or Gâteaux derivatives need not imply Fréchet differentiability.
wp-derivativenlab-derivativeEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
At each point of a differentiable function, the defining first-order approximation determines a unique continuous linear derivative.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-derivativenlab-derivativeEach relation below starts at this concept.
No direct relations are authored in this direction.