The total derivative (ou derivative in the au sense of Fréchet) exists and equals the gradient of f of a () if .

Idea

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As example R2,  , where h is a very small number, equals the sum:

  •  
  •   where   (straight line with gradient of the function at the point  )
  • the rest   which depends only of h


So   [1]

See also

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  1. ^ Analyse pour ingénieurs - semestre 2, C.A.Stuart, Lausanne, p. 25