A mathematical investigation of the general power rule and its limited applicability

Authors

  • Reaven B. Liwag Nueva Ecija University of Science and Technology, San Isidro, Nueva Ecija, Philippines
  • Mark Ren D. Villaflor Nueva Ecija University of Science and Technology, San Isidro, Nueva Ecija, Philippines
  • Micka Ella B. Anoche Nueva Ecija University of Science and Technology, San Isidro, Nueva Ecija, Philippines
  • Jaycelyn S. A. Ignacio Nueva Ecija University of Science and Technology, San Isidro, Nueva Ecija, Philippines
  • Dr. Maulina Nurfahmi Muhammadiyah University of Kendari, Kendari, Sulawesi Tenggara, Indonesia

DOI:

https://doi.org/10.64171/JAES.6.4.47-53

Keywords:

General power rule, Differential calculus, Chain rule, Mathematical investigation, Differentiation

Abstract

The General Power Rule is a fundamental differentiation technique in differential calculus that extends the Traditional Power Rule through the application of the Chain Rule to differentiate composite functions. This study investigated its mathematical foundation, applications, properties, validity, and limitations using a descriptive-analytical research design with a deductive mathematical analysis framework. Mathematical derivations, formal proofs, worked examples, symbolic manipulations, and scholarly literature served as the primary sources of theoretical evidence. The findings established that the General Power Rule is derived from the integration of the Traditional Power Rule and the Chain Rule, making it an efficient, consistent, and accurate method for differentiating composite functions. The rule was found applicable to polynomial, rational, radical, trigonometric, exponential, logarithmic, and other differentiable composite functions under appropriate mathematical conditions. However, its direct application is limited for non-differentiable, implicit, piecewise-defined, and fractional-order functions. Overall, the study confirms the General Power Rule as a reliable differentiation technique within classical differential calculus.

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Published

2026-07-15

How to Cite

Liwag, R. B., Villaflor, M. R. D., Anoche, M. E. B., Ignacio, J. S. A., & Nurfahmi, M. (2026). A mathematical investigation of the general power rule and its limited applicability. Journal of Advanced Education and Sciences, 6(4), 47–53. https://doi.org/10.64171/JAES.6.4.47-53

Issue

Vol. 6 No. 4 (2026)

Section

Articles

License

Copyright (c) 2026 Reaven B. Liwag, Mark Ren D. Villaflor, Micka Ella B. Anoche, Jaycelyn S. A. Ignacio, Dr. Maulina Nurfahmi

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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