Analysis MOC

Total derivative

The total derivative of a function at a point gives the best linear approximation of in a neighbourhood of . Let and be open, , and be differentiable. The total derivative at is the linear map defined by1 #m/def/anal

For more general spaces, see Tangent map.

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Footnotes

  1. 1997. Topology from the differentiable viewpoint, p. 3 ↩