Geodesic
The optimization of estimations of inverse function's derivative
Trudy Instituta matematiki, Tome 14 (2006) no. 1, pp. 100-107.

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In the article the estimates for high derivatives of the inverse function are presented. The results are based on the “graph” method offered earlier by the author, this method used the delicate relations between the structure of terms in the formula for derivatives of the inverse function and some “forest” of trees of special type. 
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Ju. V. Lysenko. The optimization of estimations of inverse function's derivative. Trudy Instituta matematiki, Tome 14 (2006) no. 1, pp. 100-107. http://geodesic.mathdoc.fr/item/TIMB_2006_14_1_a11/

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