Practical Use of Derivatives in Different Engineering Fields
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1-20
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Dec 12, 2025
Digital Object Identifier:
10.58578/mjaei.v3i1.8274
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Authors:
Praveen Shah1, Suresh Kumar Sahani2 
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Main Article Content
Abstract
This study examines the practical applications of derivatives as a cornerstone of engineering mathematics, enabling precise quantification of rates of change, optimization of processes, and accurate prediction of system behavior. It aims to demonstrate how derivatives are operationalized across mechanical, electrical, civil, chemical, aerospace, and computer engineering through motion analysis, structural integrity assessment, electrical circuit dynamics, chemical reaction rate calculations, flight stability analysis, and computational optimization. Employing case studies, mathematical models, and real-world examples, the paper systematizes the role of derivatives in formulating and solving engineering problems, supported by illustrative tables, formulas, and graphs that clarify key computational steps and outcomes. The findings highlight that derivatives provide a unifying analytical framework for modeling dynamic phenomena, improving design reliability, and enhancing control and optimization strategies across diverse engineering domains. The study concludes that a rigorous understanding and applied use of derivatives are essential for effective engineering analysis and decision-making, with implications for strengthening curricula in engineering mathematics and promoting derivative-based approaches in professional engineering practice.
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Shah, P., & Sahani, S. K. (2025). Practical Use of Derivatives in Different Engineering Fields. Mikailalsys Journal of Advanced Engineering International, 3(1), 1-20. https://doi.org/10.58578/mjaei.v3i1.8274
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
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Kreyszig, E. (2011). Advanced Engineering Mathematics (10th Ed.). Wiley.
Mahato, A. K., Das, R., & Sahani, S. K. (2025). Simulation of Motion in Computer Graphics Using Runge–Kutta Methods. African Multidisciplinary Journal of Sciences and Artificial Intelligence, 2(2), 325–342. https://doi.org/10.58578/amjsai.v2i2.5681
Murthy, M. S. R., Latha, M. P., & Deepthi, K. G. R. (2014). Minimizing the Waiting Time at Bank ATM for Service with Queuing Model. International Journal of Scientific Research, 3(1), 25–27.
Ogata, K. (2010). Modern Control Engineering (5th Ed.). Prentice Hall.
Sah, D. K., & Sahani, S. K. (2021). Greenhouse Gas Impact Modeling. Journal of Chemical Health Risks, 11(4), 503–509. https://doi.org/10.52783/jchr.v11.i4.8641
Sah, S., Sahani, S. K., Et Al. (2024). Some Real Life Applications of Derivatives in Economics. Mikailalsys Journal of Advanced Engineering International, 1(2), 120–131. https://doi.org/10.58578/mjaei.v1i2.2954
Sahani, S. K. (2021). Differential Equations in Astrophysics: a Fundamental Approach to Understanding Cosmic Structures and Their Dynamic Evolution. Letters in High Energy Physics, 2021, 1–13. https://doi.org/10.52783/lhep.2021.1468
Sahani, S. K. (2024). Big Data Learning Analytics and Optimization: a Numerical Perspective. Analysis and Metaphysics, 23(1), 912–924.
Sahani, S. K., & Jha, D. (2022). Study and Investigation on Real Life Application of First Ordered Differential Equation. The Mathematics Education, 56(1), 18–27.
Sahani, S. K., & Karna, S. K. (2025). Simulation of Cultural Value Clash Using Numerical Methods. Journal of Posthumanism, 4(3), 543–559. https://doi.org/10.63332/joph.v4i3.2686
Sahani, S. K., & Karna, S. K. (2025). Program for Cultural Education Optimization by the Application of Numerical Methods. Journal of Posthumanism, 5(1), 1611–1627. https://doi.org/10.63332/joph.v5i1.2687
Sahani, S. K., & Mandal, R. H. (2022). Population Growth Modeling Using RK4. International Journal of Multiphysics, 16(4), 453–461.
Sahani, S. K., & Mandal, R. H. (2022). Birth–Death Model Using Modified Euler Method. Panamerican Mathematical Journal, 32(3), 9–21.
Sahani, S. K., & Mandal, R. H. (2023). Bot Detection Using Logistic Regression and Numerical Methods. Linguistic and Philosophical Investigations, 22(2), 192–206.
Sahani, S. K., & Mandal, R. H. (2024). Predictive Analysis of Urban Population Growth Using Least Squares. International Journal of Multiphysics, 18(4), 1215–1226.
Sahani, S. K., & Mandal, R. H. (2025). Migration Effects on Regional Population Using Numerical Models. International Journal of Multiphysics, 19(1), 980–992.
Sahani, S. K., & Sah, B. K. (2021). Dynamical Systems Approach to Echo Chamber Polarization Using Laplace and RK Methods. Communications on Applied Nonlinear Analysis, 28(4), 105–113. https://doi.org/10.52783/cana.v28.5574
Sahani, S. K., & Sah, B. K. (2023). Cement Manufacturing Using Chapman–Kolmogorov Differential Equations. International Journal of Multiphysics, 17(4), 538–544.
Sahani, S. K., & Sah, B. K. (2023). Performance Assessment of Industrial Plants Using Laplace Transform and Chapman–Kolmogorov Differential Equations. Journal of Computational Analysis and Applications, 31(1), 1308–1317.
Sahani, S. K., & Sah, B. K. (2024). Social Media Customer Feedback and Product Development Analysis Using Mathematical Models. Linguistic and Philosophical Investigations, 23(1), 3038–3057.
Sahani, S. K., & Sah, B. K. (2024). Stability and Convergence Analysis of Fourth-Order Runge–Kutta Method for Nonlinear Ordinary Differential Equations. Panamerican Mathematical Journal, 34(2), 300–308.
Sahani, S. K., & Sah, B. K. (2025). Optimization of Cultural Education Program Using Numerical Techniques. Journal of Posthumanism, 5(6), 4265–4280.
Sahani, S. K., Mandal, R. H., Et Al. (2022). Age-Structured Population Dynamics Using RK Methods. Advances in Nonlinear Variational Inequalities, 25(1).
Sahani, S. K., Mandal, R. H., Et Al. (2025). Numerical Simulation of Cultural Value Conflict in Multicultural Societies. Journal of Posthumanism, 5(3), 1815–1831. https://doi.org/10.63332/joph.v5i3.2651
Sahani, S. K., Oruganti, S. K., Satish Kumar, K., & Karna, S. K. (2025). Reliability Assessment of a Plywood Production Facility Utilizing Laplace Transform and Runge–Kutta Fourth-Order Differential Equations: Overview of Industrial Plant. Metallurgical and Materials Engineering, 31(4), 417–423. https://doi.org/10.63278/1453
Sahani, S. K., Prasad, K. S., & Others. (2022). Some New Applications of Calculus to Non-Linear Sciences. Applied Science Periodical, XXIV(4), 1–9. https://doi.org/10.5281/zenodo.7865875
Sahani, S. K., Sah, B. K., & Sahani, K. (2023). Reliability-Centered Maintenance in Cement Manufacturing Plants. Advances in Nonlinear Variational Inequalities, 26(1), 16–25. https://doi.org/10.52783/anvi.v26.4224
Sahani, S. K., Sah, B. K., & Sahani, K. (2024). Mathematical Input–Output Analysis for Economic Impact Assessment: a Case Study on Local Government Bridge Construction Project. Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika, 6(2), 279–292.
Sahani, S. K., Sah, D. K. (2022). Euler’s Method: a Numerical Model for the Decomposition of Organic Waste. Journal of Computational Analysis and Applications, 30(1), 857–868.
Sahani, S. K., Sah, D. K. (2023). Hybrid Analytical–Numerical Techniques for Machine Learning Optimization: Integrating Laplace Transform and Runge–Kutta Fourth-Order Methods. Review of Contemporary Philosophy, 22, 6854–6860. https://doi.org/10.52783/rcp.1165
Sahani, S. K., Sah, M. K., Agarwal, S. K., Pareek, V., & Singh, V. V. (2020). Numerical Optimization for Public Transport Network Design. International Journal of Multiphysics, 14(4), 426–435.
Sahani, S. K., Et Al. (2018). Study and Analysis of Dynamical Models of Plant Growth Analysis in Calculus. International Journal of Engineering, Pure and Applied Sciences, 3(1), 30–35.
Sahani, S. K., Et Al. (2023). Evaluation of International Complexity of Mathematical Programming Problems. Korea Review of International Studies, 16(46), 51–55.
Sahani, S. K., Et Al. (2023). Ellipsoid Algorithm for Non-Linear Programming. Manager – the British Journal of Administrative Management, 59(163), 30–37.
Sahani, S. K., Et Al. (2023). Planetary and Stellar Motion Modeling Using Differential Equations. Arzusin Journal Manajemen Pendidikan Dasar, 3(6), 769–782.
Sahani, S. K., Et Al. (2024). Differential Equations in Aerospace Engineering: an Analytical Framework. Alsystech Journal of Education Technology, 2(1), 13–30.
Sahani, S. K., Et Al. (2024). Mathematical Modeling and Optimization of Replacement Problems. Mikailalsys Journal of Multidisciplinary, 2(1), 1–12.
Sahani, S. K., Et Al. (2025). Stationary Shop Queuing Model: an Overview of Mathematical Modeling. Panamerican Mathematical Journal, 35(1s), 335–343.
Sahani, S. K., Et Al. (2025). System Reliability and Plastic Pipe Infrastructure Using Reliability-Centered Design. International Journal of Applied Mathematics, 38(5).
Sahani, S. K., Et Al. (2025). Mechanical and Operational Behavior in Steel Manufacturing Plant. Reports in Mechanical Engineering.
Sahani, S. K., Et Al. (2022). Predicting Numerical Integration Errors Using Machine Learning. Letters in High Energy Physics, 2022, 96–103.
Sahani, S. K., Et Al. (2023). Reliability-Centered Maintenance in Cement Plants. Advances in Nonlinear Variational Inequalities, 26(1), 16–25.
Sahani, S. K., Et Al. (2023). Reliability Analysis of Rice Production Facility. Fuel Cells Bulletin, 1, 15–21. https://doi.org/10.52710/fcb.212
Sahani, S. K., Et Al. (2023). Numerical Methods in Structural Health Monitoring Using Iot. Journal of Electrical Systems, 19(1), 194–207. https://doi.org/10.52783/jes.8941
Sahani, S. K., Et Al. (2024). AI-Enhanced Finite Element Method for Structural Analysis. Journal of Electrical Systems, 20(1), 661–676. https://doi.org/10.52783/jes.8946
Sahani, S. K., Et Al. (2025). Performance Assessment of Industrial Plants: a Mathematical Framework. Dandao Xuebao/Journal of Ballistics, 37(1), 295–304. https://doi.org/10.52783/dxjb.v37.203
Stewart, J. (2015). Calculus: Early Transcendentals (8th Ed.). Cengage Learning.
Taha, H. A. (2007). Operations Research: an Introduction (8th Ed.). Pearson.
White, F. M. (2011). Fluid Mechanics (7th Ed.). Mcgraw-Hill.
Jha, A., Sahani, S. K., Et Al. (2023). From Equations to Insights: Navigating the Canvas of Tumor Growth Dynamics. Masaliq: Jurnal Pendidikan dan Sains, 3(6), 1246–1264. https://doi.org/10.58578/masaliq.v3i6.1983
Jha, A., Sahani, S. K., Et Al. (2023). Journey to the Cosmos: Navigating Stellar Evolution with Differential Equations. Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika, 5(2), 282–297.
Kreyszig, E. (2011). Advanced Engineering Mathematics (10th Ed.). Wiley.
Mahato, A. K., Das, R., & Sahani, S. K. (2025). Simulation of Motion in Computer Graphics Using Runge–Kutta Methods. African Multidisciplinary Journal of Sciences and Artificial Intelligence, 2(2), 325–342. https://doi.org/10.58578/amjsai.v2i2.5681
Murthy, M. S. R., Latha, M. P., & Deepthi, K. G. R. (2014). Minimizing the Waiting Time at Bank ATM for Service with Queuing Model. International Journal of Scientific Research, 3(1), 25–27.
Ogata, K. (2010). Modern Control Engineering (5th Ed.). Prentice Hall.
Sah, D. K., & Sahani, S. K. (2021). Greenhouse Gas Impact Modeling. Journal of Chemical Health Risks, 11(4), 503–509. https://doi.org/10.52783/jchr.v11.i4.8641
Sah, S., Sahani, S. K., Et Al. (2024). Some Real Life Applications of Derivatives in Economics. Mikailalsys Journal of Advanced Engineering International, 1(2), 120–131. https://doi.org/10.58578/mjaei.v1i2.2954
Sahani, S. K. (2021). Differential Equations in Astrophysics: a Fundamental Approach to Understanding Cosmic Structures and Their Dynamic Evolution. Letters in High Energy Physics, 2021, 1–13. https://doi.org/10.52783/lhep.2021.1468
Sahani, S. K. (2024). Big Data Learning Analytics and Optimization: a Numerical Perspective. Analysis and Metaphysics, 23(1), 912–924.
Sahani, S. K., & Jha, D. (2022). Study and Investigation on Real Life Application of First Ordered Differential Equation. The Mathematics Education, 56(1), 18–27.
Sahani, S. K., & Karna, S. K. (2025). Simulation of Cultural Value Clash Using Numerical Methods. Journal of Posthumanism, 4(3), 543–559. https://doi.org/10.63332/joph.v4i3.2686
Sahani, S. K., & Karna, S. K. (2025). Program for Cultural Education Optimization by the Application of Numerical Methods. Journal of Posthumanism, 5(1), 1611–1627. https://doi.org/10.63332/joph.v5i1.2687
Sahani, S. K., & Mandal, R. H. (2022). Population Growth Modeling Using RK4. International Journal of Multiphysics, 16(4), 453–461.
Sahani, S. K., & Mandal, R. H. (2022). Birth–Death Model Using Modified Euler Method. Panamerican Mathematical Journal, 32(3), 9–21.
Sahani, S. K., & Mandal, R. H. (2023). Bot Detection Using Logistic Regression and Numerical Methods. Linguistic and Philosophical Investigations, 22(2), 192–206.
Sahani, S. K., & Mandal, R. H. (2024). Predictive Analysis of Urban Population Growth Using Least Squares. International Journal of Multiphysics, 18(4), 1215–1226.
Sahani, S. K., & Mandal, R. H. (2025). Migration Effects on Regional Population Using Numerical Models. International Journal of Multiphysics, 19(1), 980–992.
Sahani, S. K., & Sah, B. K. (2021). Dynamical Systems Approach to Echo Chamber Polarization Using Laplace and RK Methods. Communications on Applied Nonlinear Analysis, 28(4), 105–113. https://doi.org/10.52783/cana.v28.5574
Sahani, S. K., & Sah, B. K. (2023). Cement Manufacturing Using Chapman–Kolmogorov Differential Equations. International Journal of Multiphysics, 17(4), 538–544.
Sahani, S. K., & Sah, B. K. (2023). Performance Assessment of Industrial Plants Using Laplace Transform and Chapman–Kolmogorov Differential Equations. Journal of Computational Analysis and Applications, 31(1), 1308–1317.
Sahani, S. K., & Sah, B. K. (2024). Social Media Customer Feedback and Product Development Analysis Using Mathematical Models. Linguistic and Philosophical Investigations, 23(1), 3038–3057.
Sahani, S. K., & Sah, B. K. (2024). Stability and Convergence Analysis of Fourth-Order Runge–Kutta Method for Nonlinear Ordinary Differential Equations. Panamerican Mathematical Journal, 34(2), 300–308.
Sahani, S. K., & Sah, B. K. (2025). Optimization of Cultural Education Program Using Numerical Techniques. Journal of Posthumanism, 5(6), 4265–4280.
Sahani, S. K., Mandal, R. H., Et Al. (2022). Age-Structured Population Dynamics Using RK Methods. Advances in Nonlinear Variational Inequalities, 25(1).
Sahani, S. K., Mandal, R. H., Et Al. (2025). Numerical Simulation of Cultural Value Conflict in Multicultural Societies. Journal of Posthumanism, 5(3), 1815–1831. https://doi.org/10.63332/joph.v5i3.2651
Sahani, S. K., Oruganti, S. K., Satish Kumar, K., & Karna, S. K. (2025). Reliability Assessment of a Plywood Production Facility Utilizing Laplace Transform and Runge–Kutta Fourth-Order Differential Equations: Overview of Industrial Plant. Metallurgical and Materials Engineering, 31(4), 417–423. https://doi.org/10.63278/1453
Sahani, S. K., Prasad, K. S., & Others. (2022). Some New Applications of Calculus to Non-Linear Sciences. Applied Science Periodical, XXIV(4), 1–9. https://doi.org/10.5281/zenodo.7865875
Sahani, S. K., Sah, B. K., & Sahani, K. (2023). Reliability-Centered Maintenance in Cement Manufacturing Plants. Advances in Nonlinear Variational Inequalities, 26(1), 16–25. https://doi.org/10.52783/anvi.v26.4224
Sahani, S. K., Sah, B. K., & Sahani, K. (2024). Mathematical Input–Output Analysis for Economic Impact Assessment: a Case Study on Local Government Bridge Construction Project. Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika, 6(2), 279–292.
Sahani, S. K., Sah, D. K. (2022). Euler’s Method: a Numerical Model for the Decomposition of Organic Waste. Journal of Computational Analysis and Applications, 30(1), 857–868.
Sahani, S. K., Sah, D. K. (2023). Hybrid Analytical–Numerical Techniques for Machine Learning Optimization: Integrating Laplace Transform and Runge–Kutta Fourth-Order Methods. Review of Contemporary Philosophy, 22, 6854–6860. https://doi.org/10.52783/rcp.1165
Sahani, S. K., Sah, M. K., Agarwal, S. K., Pareek, V., & Singh, V. V. (2020). Numerical Optimization for Public Transport Network Design. International Journal of Multiphysics, 14(4), 426–435.
Sahani, S. K., Et Al. (2018). Study and Analysis of Dynamical Models of Plant Growth Analysis in Calculus. International Journal of Engineering, Pure and Applied Sciences, 3(1), 30–35.
Sahani, S. K., Et Al. (2023). Evaluation of International Complexity of Mathematical Programming Problems. Korea Review of International Studies, 16(46), 51–55.
Sahani, S. K., Et Al. (2023). Ellipsoid Algorithm for Non-Linear Programming. Manager – the British Journal of Administrative Management, 59(163), 30–37.
Sahani, S. K., Et Al. (2023). Planetary and Stellar Motion Modeling Using Differential Equations. Arzusin Journal Manajemen Pendidikan Dasar, 3(6), 769–782.
Sahani, S. K., Et Al. (2024). Differential Equations in Aerospace Engineering: an Analytical Framework. Alsystech Journal of Education Technology, 2(1), 13–30.
Sahani, S. K., Et Al. (2024). Mathematical Modeling and Optimization of Replacement Problems. Mikailalsys Journal of Multidisciplinary, 2(1), 1–12.
Sahani, S. K., Et Al. (2025). Stationary Shop Queuing Model: an Overview of Mathematical Modeling. Panamerican Mathematical Journal, 35(1s), 335–343.
Sahani, S. K., Et Al. (2025). System Reliability and Plastic Pipe Infrastructure Using Reliability-Centered Design. International Journal of Applied Mathematics, 38(5).
Sahani, S. K., Et Al. (2025). Mechanical and Operational Behavior in Steel Manufacturing Plant. Reports in Mechanical Engineering.
Sahani, S. K., Et Al. (2022). Predicting Numerical Integration Errors Using Machine Learning. Letters in High Energy Physics, 2022, 96–103.
Sahani, S. K., Et Al. (2023). Reliability-Centered Maintenance in Cement Plants. Advances in Nonlinear Variational Inequalities, 26(1), 16–25.
Sahani, S. K., Et Al. (2023). Reliability Analysis of Rice Production Facility. Fuel Cells Bulletin, 1, 15–21. https://doi.org/10.52710/fcb.212
Sahani, S. K., Et Al. (2023). Numerical Methods in Structural Health Monitoring Using Iot. Journal of Electrical Systems, 19(1), 194–207. https://doi.org/10.52783/jes.8941
Sahani, S. K., Et Al. (2024). AI-Enhanced Finite Element Method for Structural Analysis. Journal of Electrical Systems, 20(1), 661–676. https://doi.org/10.52783/jes.8946
Sahani, S. K., Et Al. (2025). Performance Assessment of Industrial Plants: a Mathematical Framework. Dandao Xuebao/Journal of Ballistics, 37(1), 295–304. https://doi.org/10.52783/dxjb.v37.203
Stewart, J. (2015). Calculus: Early Transcendentals (8th Ed.). Cengage Learning.
Taha, H. A. (2007). Operations Research: an Introduction (8th Ed.). Pearson.
White, F. M. (2011). Fluid Mechanics (7th Ed.). Mcgraw-Hill.