The Applications of Derivative and Differential

Authors

  • Zilin Nie

DOI:

https://doi.org/10.61173/sjvhcy05

Keywords:

Derivative, differential, applications

Abstract

Differential and derivative are core concepts in analytical mathematics and are closely related. To be brief, the derivative refers to the rate of change of a function near a point, while the differential describes the actual change in the value of the function under the action of the derivative. Together, they form the basis of calculus. Differential is an application of the concept of derivative, specifically the response to a small change in the function. The derivative is the slope of the local linear approximation, while the differential is the increment of the function value under this linear approximation. This paper mainly discusses the topic about derivative and differential. To illustrate them clearly, this paper will introduce step by step, from their concept to examples, including definition, properties and geometric meaning. Specifically, the article particularly emphasizes applications in sequence problems and approximate calculations. These applications are of great significance in mathematics, physics, engineering, and economics.

References

[1] Tian X. Research on the application of derivatives [J]. Journal of Taiyuan Normal University: Natural Science Edition, 2000, (3): 32-33.

[2] Zheng Y. Logarithmic differentials and their application advantages in approximate calculations [J]. Journal of Qingdao University of Technology, 2003, 024(001): 63-67.

[3] Tang Y. Application of mathematical ideas in derivative problems [J]. Teaching and Learning of High School Mathematics, 2011, (8X):3.

[4] Cao J. Research on the application of calculus in university physics teaching [J]. Journal of Chifeng University: Natural Science Edition, 2013(9): 2.

[5] Wang D., Zhang W., Liu Y. Application of differential quadrature method in engineering structural dynamics[J]. Journal of Tianjin University of Science and Technology, 2018, 33(1):8.

[6] Wang B. Parameter problem in derivative application[J]. Mathematics for Middle School Students, 2021, 000(019): 20- 22.

[7] Darmayanti R., Baiduri B., Sugianto R. Learning application derivative algebraic functions: Ethnomathematical studies and digital creator books[J]. Jurnal Cendekia: Jurnal Pendidikan Matematika, 2022, 6(2): 2212-2227.

[8] Tunç, O., Tunç, C. Solution estimates to Caputo proportional fractional derivative delay integro-differential equations. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat, 2023,117: 12.

[9] Li D. Application of derivatives in proof of inequality[J]. Journal of Guiyang University: Natural Science Edition, 2014, (1): 5.

[10] Fan Y. Application of derivatives in studying sequence problems with examples[J]. Mathematical Physics and Chemistry Learning: High School Edition, 2012, (2):3.

[11] Department of Mathematics, East China Normal University. Mathematical Analysis. 4th Edition[M]. Higher Education Press, 2010.

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Published

2024-12-31

Issue

Vol. 2 No. 6 (2024): Volume 2, Issue 6

Section

Articles

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