Geodesic
Tangential vectors for sets defined with systems of equations
Trudy Instituta matematiki, Tome 20 (2012) no. 1, pp. 42-49

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The general reduction principle in the problem on tangential vectors at a fixed point for a set defined with a finite system of equations is stated. This principle reduce the original problem to the similar one however with the zero first derivative. For the reduced problem the conditions when tangential vectors are determined with the properties of the second derivative are described. 
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P. P. Zabreiko. Tangential vectors for sets defined with systems of equations. Trudy Instituta matematiki, Tome 20 (2012) no. 1, pp. 42-49. http://geodesic.mathdoc.fr/item/TIMB_2012_20_1_a4/