Generalized Definition of the Derivative

Mehmet Pakdemirli

doi:10.20944/preprints202403.1807.v1

Preprint Technical Note Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 28 March 2024 / Approved: 29 March 2024 / Online: 29 March 2024 (09:56:14 CET)

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

Limit Definition; Derivative; Error Analysis; Scaling Transformations; Translational Transformations

Computer Science and Mathematics, Applied Mathematics

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Generalized Definition of the Derivative

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